WASHINGTON  OBSERVATIONS  FOR  1870.— APPENDIX  I. 


REMOTE  ST 


f  -  y4  ^ 


REPORT 


ON  THE 


DIFFERENCE  OF  LONGITUDE 


BETWEEN 


WASHINGTON  AND  ST.  LOUIS. 

BY 

WILLIAM  HARKNESS, 

PROFESSOR  OF  MATHEMATICS,  U.  S.  NAVY. 


PREPARED  AT  THE  U.  S.  NAVAL  OBSERVATORY 

BY  ORDER  OF 

REAR-ADMIRAL  B.  F.  SANDS,  U.  S.  N., 

SUPERINTENDENT. 


WASHINGTON: 

GOVERNMENT  PRINTING  OFFICE. 

1872. 


Vi  Lt 


c^S  Z.G?.£2- 


TABLE  OF  CONTENTS. 


Page. 


I.  Introductory . 5 

II.  Description  of  observing-stations . 5 

III.  Instruments  employed  at  Washington . 6 

IV.  Instruments  employed  at  St.  Louis . 6 

V.  Method  of  reducing  the  observations  for  time  : 

Formulae  employed . 7 

Adopted  mean  right  ascensions  for  1870.0  of  stars  used  in  the  determination  of  the  difference  of  longitude 
between  Washington  and  St.  Louis,  together  with  the  constants  for  azimuth,  level,  and  collimation  at  each 

station . ' . 8 

Observations  for  time  at  Washington . 10 

Resulting  corrections  to  the  Kessels  clock . 14 

Observations  for  time  at  St.  Louis . 15 

Resulting  corrections  to  the  chronometer  Dent  No.  274S . 22 

VI.  Personal  equation . 23 

Relative  personal  equation  of  Mr.  Frisby  and  Professor  Harkness . 33 

Relative  personal  equation  of  Professors  Eimbeck  and  Harkness . 33 

VII.  Exchange  of  time-signals,  and  resulting  difference  of  longitude: 

The  Telegraph  line  between  Washington  and  St.  Louis . 34 

Programme  for  the  exchange  of  signals . 35 

Formulae  emplojmd  for  the  reduction  of  the  signals . 37 

Comparisons  of  time-pieces  obtained  by  reading  off  the  Washington  chronograph-sheets . 38 

Comparisons  of  time-pieces  obtained  by  observing  coincidences  of  beats  at  St.  Louis . 38 

Clock  and  chronometer  corrections  at  the  times  of  the  exchange  of  signals . 39 

Observed  values  of  the  difference  of  longitude  between  Washington  and  St.  Louis,  and  of  the  time  occupied 

in  the  passage  of  a  galvanic  signal  between  those  cities . . 39 

Final  value  of  the  difference  of  longitude  between  Washington  and  St.  Louis . 39 


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https://archive.org/details/reportondifferenOOhark 


REPORT 


ON  THE 

DIFFERENCE  OF  LONGITUDE 

BETWEEN 


WASHINGTON  AND  ST.  LOUIS. 


United  States  Naval  Observatory, 

Washington ,  November  14,  1872. 

Sir:  I  have  the  honor  to  submit  to  you  the  following'  report  on  the  determination 
of  the  difference  of  longitude  between  Washington  and  St.  Louis,  of  which  you  directed 
me  to  take  charge  so  far  as  this  Observatory  is  concerned. 

I.— INTRODUCTORY. 

The  operations  described  in  this  report  were  initiated  by  the  United  States  Coast 
Survey,  and  the  Observatory  took  part  in  them  at  the  request  of  that  institution,  with 
the  understanding  that  the  observations  at  St,  Louis  should  be  made  by  Coast  Survey 
officers,  and  those  at  Washington  by  Observatory  officers;  and  that  at  the  conclusion 
of  the  campaign  complete  copies  of  the  observations  and  reductions  should  be  exchanged 
for  each  other’s  use.  The  observations  here  were  made  by  myself  and  Assistant  Ob¬ 
server  Edgar  Frisby,  and  reduced  entirely  by  me.  The  observations  at  St.  Louis  were 
made  by  Professor  William  Eimbeck,  of  the  Coast  Survey,  and  reduced  by  Professor 
R.  Keith,  of  the  Coast  Survey;  but,  as  the  right  ascensions  which  the  latter  gentleman 
adopted  for  some  of  the  stars  employed  differed  slightly  from  those  used  at  this  Ob¬ 
servatory,  before  his  work  could  be  compared  with  my  own  it  required  a  few  small 
corrections,  which  have  been  introduced  by  Mr.  Frisby  and  myself.  The  arrange¬ 
ments  for  the  use  of  the  Western  Union  Telegraph  Company’s  lines  between  Wash¬ 
ington  and  St.  Louis  were  made  by  the  officers  of  the  Coast  Survey,  but  I  cannot 
refrain  from  expressing  my  thanks  to  Mr.  M.  Marean,  the  Western  Union  Company’s 
electrical  superintendent  in  this  city,  for  his  kindness  in  promptly  making  the  neces¬ 
sary  connections  between  the  different  wires  at  the  main  office  here. 

II.— DESCRIPTION  OF  OBSERVIN G-STATION S. 

The  observing-station  at  Washington  was  the  present  site  of  the  transit  circle, 
which  is  77.8  feet  due  west  of  the  center  of  the  dome  of  the  Observatory.  Its  geogra¬ 


phical  position  is: 

Latitude, . +3S°53/  3  8".  8 

Longitude,  west  of  Greenwich,  .  5h  8rai2s.o 


The  station  at  St,  Louis  was  in  a  small  observatory  erected  on  St.  Charles  street, 
between  Seventeenth  and  Eighteenth  streets,  in  the  southwest  corner  of  the  Wasliing- 
ton  University  grounds.  These  grounds,  rectangular  in  form,  are  bounded  on  the  north 


6 


DIFFERENCE  OF  LONGITUDE, 


by  Washington  avenue,  and  on  the  south  by  St.  Charles  street,  occupying  the  whole 
space  between  these  streets,  which  is  150  feet.  They  are  bounded  on  the  east  by 
Seventeenth  street,  and  extend  206  feet  10^  inches  toward  Eighteenth  street.  Wash¬ 
ington  avenue  and  St.  Charles  streets  are  parallel  to  each  other,  and  run  in  the  direction 
south  75°  east.  Seventeenth  and  Eighteenth  streets  are  also  parallel  to  each  other  and 
run  in  the  direction  south  150  west.  The  small  observatory  building  measured  eight 
feet  from  north  to  smith,  and  ten  feet  from  east  to  west.  It  contained  two  piers,  the 
transit  instrument  being  mounted  on  the  eastern  one  and  the  zenith  telescope  on  the 
western  one.  The  following  distances  were  measured  from  the  station  point  on  the 
transit  pier,  viz:  to  the  western  boundary  of  the  university  grounds,  13  feet  5  inches; 
to  the  line  of  curb-stones  on  the  northern  side  of  St.  Charles  street,  14  feet  4  inches: 
and  to  the  produced  western  face  of  the  Scientific  Department  building,  10  feet  4 
inches.  The  approximate  latitude  of  the  station  was  +  38°  37'. 


III.— INSTRUMENTS  EMPLOYED  AT  WASHINGTON. 


The  Transit  Circle,  whose  object-glass  has  a  focal  length  of  145  inches,  and  a  clear 
aperture  of  8.52  inches,  was  used  with  an  eye-piece  which  produced  a  magnifying-power 
of  186  diameters.  Throughout  the  whole  series  of  observations  the  clamp  end  of  the 
axis  was  to  the  east.  A  description  of  this  instrument  is  given  in  Appendix  I  to  the 
Washington  Observations  for  1865. 

J  he  Kessels  Side)  cal  (  loch,  No.  1 3 2 4 ?  which  is  the  Observatory  standard,  was 
employed  in  connection  with 

A.  CJn  onoyraph,  having  a  barrel  8.15  inches  in  diameter  and  24.0  inches  long-, 
revolving  once  each  minute.  This  chronograph  will  run  continuously  for  four  hours 
without  requiring  the  paper  to  be  changed.  It  has  but  a  single  pen,  with  which  both 
the  clock-signals  and  those  made  by  the  observer  are  recorded. 

The  Electro-magnetic  Apparatus,  which  was  used  for  sending  and  receiving  the 
longitude-signals  is  entirely  automatic.  It  would  occupy  too  much  space  to  explain  it 
here,  but  a  full  description  may  be  found  in  Appendix  I  to  the  Washington  Observations 
for  1867. ' 


I Y.— INSTRUMENTS  EMPLOYED  AT  ST.  LOUIS. 

United  States  Coast  Survey  Portable  Transit  Instrument  No.  7,  made  by  William 
A  iirdemann,  of  Washington.  Its  object-glass  has  a  focal  distance  of  25^  inches,  and 
a  clear  aperture  of  2.03  inches.  A  diagonal  eye-piece  was  used,  wliicli  produced  a 
magnifying-power  of  67  diameters.  The  length  of  the  axis  between  the  Y’s  is  1 4  inches, 
and  the  pivots  are  0.71  of  an  inch  in  diameter.  It  is  provided  with  two  finding-circles, 
each  4  inches  in  diameter,  graduated  to  every  2c/,  and  reading  by  means  of  two  ver¬ 
niers  to  single  minutes. 

A  Sidereal  Box  Chronometer,  Kessels  and  Dent  No.  1287. 

A  Mean  Time  Box  Chronometer,  Dent  No.  2748. 

1  he  Elect)  o-may net ic  Apparatus  employed  was  the  ordinary  Morse  receiving  mao- 
net,  sounder,  and  key,  together  with  a  break-circuit  key;  all  of  which  were  in  the 
Western  Union  Telegraph  Office  in  the  Merchant’s  Exchange,  on  First  street,  between 
Walnut  and  Market  streets. 


WASHINGTON  AND  ST.  LOUIS. 


7 


Y.-METHOD  OF  REDUCING  THE  OBSERVATIONS  FOR  TIME. 

Let 

a  —  apparent  right  ascension  of  the  star  observed; 

T'  —  observed  clock  or  chronometer  time  of  star’s  transit ; 

T0  —  time,  by  face  of  clock  or  chronometer,  for  which  clock  or  chronometer 
correction  is  to  be  determined; 

R  —  rate  per  hour  of  clock  or  chronometer; 

A T0  —  correction  of  clock  or  chronometer  at  the  instant  when  its  face  indi¬ 
cated  the  time  T0- 
v  —  effect  of  errors  of  observation ; 

«,  b,  and  c  —  respectively,  the  azimuth,  level,  and  collimation  constants; 

A,  B  ,and  C  —  respectively,  the  azimuth,  level,  and  collimation  factors, 

Then  each  star  observed  will  furnish  one  equation  of  condition  of  the  form 
o=  a  -  \_T  +  ^T0  +  R  (T'-T0)  +  Aa  +  Bb  +  Cc]  -  v 
and  from  all  the  equations  thus  obtained  the  most  probable  values  of  the  quantities 
considered  as  unknown  can  be  found  by  the  method  of  least  squares. 

When  the  observations  have  been  made  with  a  fixed  instrument,  the  quantities 
sought  are  usually  AT0  and  R\  but  if  a  portable  instrument  has  been  used  they  will 
generally  be  AT0,  R,  and  a.  Sometimes  it  is  convenient  to  make  T0  equal  to  the 
mean  of  the  observed  times  of  transit  of  all  the  stars  in  the  group,  and  then  R  is  found 
from  the  difference  between  the  values  of  AT0  given  by  two  groups  of  stars  separated 
by  an  interval  of  some  hours.  It  is  always  advantageous  to  have  the  unknown  quan¬ 
tities  in  the  equations  of  condition  quite  small,  and  therefore,  when  possible,  it  is  best 
to  introduce  closely  approximate  values  of  these  quantities,  and  to  solve  only  for  small 
corrections  to  these  approximate  values.  Thus,  if  R  is  large,  and  r  is  an  approximate 
value  of  it,  we  write  R  —  dr  -f-r,  and,  substituting  that  value  in  the  equations  of  con¬ 
dition,  we  determine  dr.  In  the  same  manner,  if  A  T{)  is  large,  and  0  is  an  approxi¬ 

mate  value  of  it,  we  write  AT0  —  9  -f-  69,  and,  substituting  that  value  in  the  equations 
of  condition,  we  determine  69. 

The  factors  A,  B ,  and  C  may  be  computed  by  means  of  the  formulae 
A  —  sin  ( —  d)  sec  d  —  sin  —  cos  g>  tan  d 

B  —  cos  ( —  d )  sec  d  —  cos  cp  -f-  sin  cp  tan  d 

C  —  sec  d 

in  which  cp  is  the  latitude  of  the  place  of  observation,  and  d  the  declination  of  the  star 
observed.  For  a  culmination  below  the  pole,  180°  —  d  must  be  substituted  instead  of 
d.  The  following  rules  are  sometimes  convenient  for  determining  the  signs  of  these 
quantities. 

A  is  positive,  except  for  stars  between  the  zenith  and  the  pole. 

B  and  C  are  positive,  except  for  stars  below  the  pole. 

Table  I  gives  the  adopted  mean  places  of  all  the  stars  employed  in  the  longitude 
operations,  together  with  the  corresponding  values  of  A,  B,  and  C,  both  at  Washington 
and  St.  Louis. 


8 


DIFFERENCE  OF  LONGITUDE, 


Table  I. — Adopted  Mean  Bight  Ascensions  for  1870.0  of  Stars  used  in  the  Determination 
of  the  Difference  of  Longitude  between  Washington  and  St.  Louis ;  together  with  the 
Constants  A,  D,  and  C  for  Azimuth,  Level,  and  CoUimation  at  each  Station. 


Name  of  Star. 

Right  Ascension. 

Washington. 

St.  Louis. 

A 

B 

c 

A 

B 

c 

h. 

m. 

s. 

£ 

Ilydrae  .... 

8 

39 

53-45 

+ 

0.529 

+ 

0.857 

+ 

1 .01 

L 

Ursae  Majoris  . 

8 

50 

17.72 

- 

0.247 

+ 

1.490 

+ 

1.52 

K 

Cancri  .... 

9 

0 

42.25 

+ 

0.462 

+ 

0.918 

+ 

1.03 

I 

Draconis 

9 

18 

20.13 

- 

4-85 

+ 

5-15 

+ 

7.08 

a 

Ilydrae  .... 

9 

21 

11.96 

+ 

0.734 

+ 

0.693 

+ 

1. 01 

p 

Cephei,  S.  P. 

9 

26 

58.46 

+ 

2.76 

_ 

0-939 

— 

2.92 

£ 

Leonis  .... 

9 

38 

28.10 

+ 

0.267 

+ 

1.06 

+ 

1 . 10 

1“ 

Leonis  .... 

9 

45 

21.94 

+ 

0.232 

+ 

1.09 

+ 

I.  12 

79 

Draconis,  S.  P.  .  . 

9 

51 

15.02 

+ 

3.19 

- 

1.27 

- 

3-44 

a 

Leonis  .... 

10 

1 

26.82 

+ 

0.449 

+ 

0.920 

+ 

1.02 

32 

Ursae  Majoris  . 

10 

8 

33-82 

— 

I  .11 

+ 

2.17 

+ 

2-44 

71 

Leonis  .... 

10 

12 

48.14 

+ 

o.33i 

+ 

1.02 

1.07 

9 

Draconis 

10 

23 

58.40 

- 

2.60 

+ 

3-36 

+ 

4-25 

l 

Leonis  .... 

10 

42 

25-37 

+ 

0.469 

+ 

0.904 

+ 

1.02 

L 

Cephei,  S.  P. 

10 

45 

3-53 

+ 

2.34 

— 

0.589 

— 

2.41 

a 

Ursae  Majoris  . 

10 

55 

41.04 

— 

0.875 

+ 

1.98 

+ 

2.16 

cJ 

Leonis  .... 

II 

7 

11.52 

.  . 

+ 

0.320 

+ 

1.02 

+ 

1.07 

5 

Crateris  .... 

II 

12 

50.58 

. 

. 

.  . 

+ 

0.S20 

+ 

0.624 

+ 

1.03 

r 

Leonis  .... 

II 

21 

15-13 

+  0.579 

+ 

0.817 

+ 

1. 00 

+ 

0.574 

+ 

0.820 

+ 

I. OO 

1 

Draconis 

II 

23 

39-55 

• 

• 

•  V 

— 

i-53 

+ 

2.50 

4" 

2.93 

V 

Leonis  .... 

II 

30 

17.60 

+  0.629 

+ 

0.777 

+ 

1 .00 

p 

Leonis  .... 

II 

42 

25.66 

+  0.416 

+ 

0.949 

+ 

1.04 

+ 

0.4II 

+ 

0.952 

+ 

1.04 

y 

Ursae  Majoris  . 

II 

46 

58.98 

• 

. 

.  . 

- 

0.468 

+ 

1.65 

+ 

1.72 

0 

Virginis. 

II 

58 

35-22 

+  0.498 

4~ 

0.883 

1 .01 

+ 

0-493 

+ 

0.886 

+ 

1 .01 

4 

Draconis 

12 

6 

4.78 

• 

* 

•  • 

— 

3- 16 

+ 

3.81 

+ 

4-95 

V 

Virginis  .... 

12 

13 

15-35 

+  0.627 

+ 

0.779 

+ 

1. 00 

+ 

0.622 

+ 

0.782 

+ 

I  .OO 

P 

Corvi . 

12 

27 

33-74 

+  0.953 

+ 

0.515 

+ 

1.08 

a 

Draconis 

12 

27 

55-31 

. 

. 

.  . 

- 

1.58 

+ 

2.54 

+ 

3.00 

12 

Canum  Venaticorum 

12 

49 

56.63 

—  0.002 

+ 

r.  29 

+ 

1.29 

e 

Virginis  .... 

13 

3 

13-27 

+  0.694 

+ 

0.725 

+ 

1. 00 

Polaris,  S.  P.  . 

13 

II 

17-34 

+32.85 

25,22 

_ 

41.42 

a 

Virginis  .... 

13 

18 

20.85 

+  0.772 

+ 

0.660 

+ 

1.02 

? 

Virginis  .... 

13 

28 

4.26 

+  0.626 

+ 

0.779 

4- 

I  .OO 

V 

Bootis  .... 

13 

48 

29.71 

+  0.360 

+ 

0.995 

+ 

1.06 

a 

Bootis  .... 

14 

9 

43-98 

+  0.347 

+ 

1 .00 

+ 

1.06 

WASHINGTON  AND  ST.  LOUIS. 


9 


Table  1.— Adopted  Mean  Right  Ascensions  for  1870.0,  dee. — Continued. 


Name  of  Star. 

Right  Ascension. 

Washington. 

St. 

Louis. 

A 

B 

c 

A 

B 

c 

h. 

m. 

s. 

£ 

Bootis . 

14 

39 

18.61 

+ 

0.219 

+  1. 11 

+ 

1. 13 

a. 2 

Librae . 

14 

43 

41.42 

+ 

0.842 

+  0.606 

+ 

I.04 

+ 

O.S38 

+ 

0.610 

+ 

1.04 

ft 

Ursae  Minoris  . 

14 

51 

6.66 

- 

2.13 

+ 

3.06 

+ 

3-79 

p 

Bootis . 

14 

57 

2 . 89 

— 

0.046 

+  1.32 

+ 

1.32 

- 

0.052 

+ 

1.32 

+ 

1.32 

ft 

Librae . 

15 

10 

0.87 

+ 

0.750 

+  0.679 

+ 

1 .01 

+ 

0.746 

+ 

0.683 

+ 

I  .OI 

p 

Bootis . 

15 

19 

34-84 

+ 

0.023 

+  1.27 

+ 

1.27 

+ 

0.017 

+ 

1.27 

+ 

1.27 

y2 

Ursae  Minoris  . 

15 

20 

57-15 

. 

. 

— 

1.82 

+ 

2.74 

+ 

3-29 

Cl 

Coronae  Borealis  . 

15 

29 

11.08 

+ 

0.229 

+  1. 10 

+ 

1 . 12 

+ 

0.223 

+ 

I  .  10 

+ 

I  .12 

a 

Serpentis  .... 

15 

37 

51.99 

+ 

0-535 

+  0.853 

+ 

I  .01 

+ 

0.530 

+ 

0.856 

+ 

I  .OI 

e 

Serpentis  .... 

15 

44 

20.27 

+ 

0.562 

+  0.832 

+ 

I  .OO 

+ 

0.557 

+ 

0 

00 

CO 

4- 

+ 

I  .00 

c 

Ursae  Minoris  . 

15 

48 

45.50 

— 

3.12 

+ 

3-77 

+ 

4.89 

e 

Coronae  Borealis  . 

15 

52 

12.44 

•  . 

+ 

0.222 

+ 

1 .  102 

+ 

I  .  12 

ft1 

Scorpii . 

15 

57 

52.89 

+ 

0.899 

0.559 

+ 

1.06 

Groombridge  2320. 

l6 

5 

58.46 

- 

i-33 

+ 

2.33 

+ 

2.69 

<5 

Ophiuchi  .... 

l6 

7 

32.12 

+ 

0.676 

+ 

0.739 

+ 

I  .OO 

r 

Ilerculis  .... 

l6 

15 

50.13 

— 

0. 189 

+ 

1.44 

+ 

1.46 

V 

Draconis  .... 

l6 

22 

14.18 

- 

0.836 

+ 

1.94 

+ 

2. 12 

c 

Ophiuchi  .... 

l6 

30 

0.16 

+ 

0.764 

+ 

0.668 

+ 

1.02 

V 

Ilerculis  .... 

l6 

38 

26.43 

- 

0.005 

+  1.29 

+ 

I  .  29 

- 

O.OII 

+ 

I  .  29 

+ 

I.29 

K 

Ophiuchi  .... 

l6 

51 

30-97 

+ 

0-497 

+  0.884 

+ 

I  .OI 

+ 

0.492 

+ 

0.887 

I  .OI 

d 

Herculis  .... 

l6 

56 

48.28 

+ 

O.  107 

+  1.20 

+ 

1.20 

+ 

0.  IOI 

+ 

1.20 

+ 

1.20 

e 

Ursae  Minoris  . 

l6 

59 

22.74 

- 

5-09 

+  5-39 

+ 

7.42 

- 

5.12 

+ 

5-37 

+ 

7.42 

a1 

Herculis  .... 

17 

8 

43.26 

+ 

0.426 

+  0.941 

+ 

1.03 

+ 

0.421 

+ 

0.944 

+ 

1.03 

44  Opliiuchi  .... 

17 

18 

26.00 

+ 

0-974 

+  0.498 

+ 

I.09 

+ 

0.971 

+ 

0.502 

+ 

I.09 

Groombridge  966,  S.  P. 

17 

22 

21.68 

+ 

3-53 

— 

i-54 

— 

3.85 

a 

Ophiuchi  .... 

17 

28 

54.07 

+ 

0.453 

+  0.919 

+ 

I  .02 

+ 

0.448 

+ 

0.922 

+ 

1.02 

0) 

Draconis  .... 

17 

37 

42.96 

- 

i-39 

+ 

2-39 

+ 

2.77 

r- 

Herculis  .... 

4i 

22.32 

+ 

0.2x6 

+  1. 11 

+ 

1. 13 

y 

Draconis  .... 

17 

53 

35-37 

.  « 

- 

3.60 

+ 

1-57 

+ 

I  .6l 

y 2 

Sagittari  .... 

17 

57 

27.50 

+ 

1.08 

+  0.413 

+ 

I .  l6 

P 

Sagittar  i  i  .... 

18 

5 

59-38 

+ 

0.926 

+  0.538 

+ 

1.07 

+ 

0.923 

+ 

0.542 

+ 

1.07 

(j 

Ursae  Minoris  . 

18 

14 

16.33 

12.47 

+  II-35 

+ 

16.86 

—12.52 

+  11.28 

+ 

16.86 

V 

Serpentis  .... 

18 

14 

35-03 

+ 

0.663 

+ 

0.749 

+ 

I  .OO 

I 

Aquilae . 

18 

28 

8.00 

+ 

0.742 

+  0.686 

+ 

1. 01 

a 

Lyrae . 

18 

32 

32.26 

+ 

0.006 

+  1.28 

+ 

1.28 

51 

Cepliei,  S.  P. 

18 

38 

43-17 

+  16.73 

—  12.21 

— 

20.  72 

+  16.86 

— 

12.  iS 

— 

20.  72 

ft 

Lyrae . 

18 

45 

16.87 

+ 

O.  117 

+  1. 19 

+ 

1. 19 

c 

Aquilae . 

18 

59 

26. 14 

+ 

0.438 

+  0.930 

+ 

I.O3 

+ 

0.433 

+ 

0-933 

+ 

1.03 

Sagittarii  .... 

19 

10 

1.68 

+ 

0.894 

+ 

0.564 

+ 

1 .06 

(5 

Aquilae . 

19 

18 

56.64 

+ 

0.589 

+  0.809 

+ 

I  .00 

+ 

0.584 

+ 

0.812 

+ 

I  .OO 

2— W  S 


4 


IO 


DIFFERENCE  OF  LONGITUDE, 


I  able  I.  Adopted  Mean  Right  Ascensions  for  1870.0,  dee. — Continued. 


Name  of  Sta 


k  Aquilae  . 
y  Aquilae  . 
rc  Aquilae  . 
ft  Aquilae  . 

%  Ursx  Minoris 

«*  Capricorni  . 
e  Delphini 
«  Cygni 
e  Aquarii  . 
v  Cygni 

1  Pegasi  . 
ft  Aquaiii  . 


Righ 

Ascension. 

Washington. 

St.  Louis. 

A 

B 

C 

A 

B 

C 

h. 

111. 

s. 

J9 

29 

53-85 

4-  0.728 

+ 

0.697 

'  + 

I  .01 

+ 

0.724 

+  0.701 

+ 

I  .OI 

19 

40 

4-79 

+  0.486 

+ 

0.892 

+ 

1.02 

+ 

0.481 

+  0.895 

+ 

1.02 

19 

4.4 

26.46 

+  0.511 

+ 

0.872 

"!* 

I  .OI 

+ 

0.506 

+  0.875 

+ 

I  .OI 

19 

48 

55-68 

+  O.545 

+ 

0.845 

+ 

I  .01 

+ 

0.540 

+  O.848 

+ 

I  .OI 

19 

54 

16.90 

-40.52 

+  33-99 

+ 

52.89 

40.68 

+  33-78 

+ 

52.89 

20 

IO 

50.44 

+  0.806 

+ 

0.634 

+ 

1.03 

_1_ 

0.802 

+  0.638 

+ 

1.03 

20 

27 

0.17 

+  0.4/8 

+ 

0.898 

+ 

1.02 

+ 

0.473 

+  0.901 

+ 

1.02 

20 

37 

0.07 

— 

O.  140 

+  1.40 

+ 

1. 41 

20 

45 

38.47 

+ 

0.747 

+  0.674 

+ 

I  .01 

20 

52 

19.70 

0.046 

+  1.32 

+ 

1.32 

21 

l6 

4-52 

+  0.357 

+ 

0-997 

+ 

1.06 

21 

24 

42.90 

+  0.712 

+ 

0.710 

+ 

I  .01 

Washington  Observations.— The  observations  for  time  made  at  Washington  are  given 
in  table  II.  I  lie  first  and  second  columns  do  not  require  any  explanation.  The 

column  “Observer”  contains  the  initials  of  the  person  who  made  the  observations,  as 
follows : 


Ha. 

E. 

F. 
S. 


Professor  William  Harkness. 
Professor  John  If.  Eastman. 
Assistant  Observer  Edgar  Erisby. 
Assistant  Observer  Ormond  Stone. 


llie  column  “J\  0.  of  Wires"  gives  the  number  of  wires  over  which  the  transit  of 
the  star  was  observed.  All  time-stars  were  observed  by  the  chronographic  method, 
and,  as  a  rule,  over  nine  wires;  but  azimuth-stars  were  observed  by  eye  and  ear,  and 
generally  over  only  five  wires.  The  column  “  Time  of  Transit  over  Mean  of  Wires ”  con¬ 
tains  the  time  of  transit  over  an  imaginary  wire  situated  at  the  mean  of  the  standard  set 
of  nine  wires..  1  or  stars  observed  over  all  the  wires  of  that  set  the  mean  of  the  observed 
tune*  of  transit  is  of  course  the  time  of  transit  over  the  mean  wire,  but  for  other  stars  the 
time  of  transit  over  the  mean  wire  has  been  deduced  from  the  observed  times  of  transit 
by  the  application  of  the  necessary  corrections.  The  columns  “Cc,”  “Bbf  and  “ Aa ” 
contain  the  corrections  for  collimation,  level,  and  azimuth.  The  numbers  in  the  column 
Correction  for  Instrument"  are  the  sums  of  the  quantities  in  the  three  preceding  cob 
umns.  I  he  column  Corr.  lransit  ’  contains  the  clock-time  of  transit  over  the  merid= 
ian,  obtained  by  adding  together  the  quantities  in  the  columns  “Time  of  Transit  over 
Mean  of  Wires"  and  “  Correction  for  Instrument."  The  column  “Adopted  Right  Ascen¬ 
sion"  contains  the  adopted  apparent  right  ascensions  of  the  stars  observed.  The  column 
“Observed  Clock  Corr."  contains  the  difference  between  the  “Corr.  Transit"  and  the 


WASHINGTON  AND  ST.  LOUIS. 


“ Adopted  Right  Ascension."  The  column  v  contains  the  difference  between  the  observed 
and  adopted  clock  corrections;  or,  in  other  words,  the  error  of  observation. 

The  values  of  the  constants  employed  during  each  night  are  as  follows: 


Date. 

c 

b 

a 

s. 

s. 

s. 

April  12 

—  0.02 

-  0.15 

+  0.02 

23 

.01 

.14 

-  0.15 

# 

26 

.02 

.08 

.07 

30 

—  0.02 

—  O.II 

—  0.16 

The  constant  c  was  obtained  from  observations  on  a  pair  of  opposing  collimators. 
Ij  was  obtained  from  observations  of  the  spirit-level,  two  readings  being  made  with  it 
in  a  direct,  and  two  with  it  in  a  reversed  position,  a  was  computed  from  the  observed 
transits  of  Polaris,  using  for  that  purpose  a  closely  approximate  value  of  the  clock 
correction.  Full  details  as  to  the  methods  of  determining  these  constants  are  given  on 
pages  xxvi— xxviii  of  the  Washington  Observations  for  1870. 


DIFFERENCE  OF  LONGITUDE, 


I  2 

Table  II. —  Transits  of  Stars  observed  at  Washington  to  determine  the  Corrections  to  the 

J vessels  Sidereal  Clock. 


Date. 

Star. 

Observer. 

No.  of  Wires. 

Time  of 

Transit  over 
Mean  of  Wires. 

Cc 

Bb 

A  a 

Correction  for 

Instrument. 

Corr.  Transit. 

Adopted  Right 
Ascension. 

Observed 
Clock  Corr. 

V 

1870. 

h. 

m. 

s. 

s. 

s. 

s. 

s. 

s. 

s. 

s. 

April  12 

T 

Leonis 

Ha. 

9 

I  I 

21 

18.  II 

—  0.  12 

—  0.  12 

+  0.01 

—0.13 

17.98 

16.00 

-1.98 

+  .02  | 

V 

Leonis 

Ha. 

9 

30 

20.54 

.02 

.  12 

.01 

-*3 

20.41 

18.51 

1.90 

—  .06 

P 

Leonis 

Ha. 

9 

42 

28.72 

.02 

.14 

.01 

•  15 

28.57 

26.57 

2.00 

+  .04 

0 

Virginis  . 

Ha. 

9 

II 

58 

38.29 

.02 

-13 

.01 

.14 

38.15 

36.20 

i-95 

—  .02 

V 

Virginis  . 

Ha. 

9 

12 

13 

18.50 

.02 

.  12 

.01 

•13 

18.37 

16.37 

2.00 

+  .03 

e 

Virginis  . 

Ha. 

9 

13 

3 

16.48 

—  .02 

—  0.  II 

.01 

—  O.  12 

16.36 

14-39 

1.97 

—  .01 

Polaris,  S.  P.  . 

Ha. 

5 

13 

10 

29.50 

+0.83 

+  3-78 

+0.66 

+  5-27 

34-77 

32.75 

—  2.02 

April  23 

V 

Leonis 

F. 

9 

1 1 

30 

24.28 

—  0.01 

—  0.  II 

—  O.O9 

—  0.21 

24.07 

18.45 

—5-62 

—  .01 

p 

Leonis 

F. 

9 

42 

32.40 

.01 

•  13 

.06 

.20 

32.20 

26.51 

.69 

+  .05 

0 

Virginis  . 

F. 

9 

1 1 

58 

41.96 

.01 

.12 

.07 

.20 

41.76 

36.15 

.6l 

-.04 

V 

Virginis  . 

F. 

9 

12 

13 

22.21 

.01 

.11 

-  .09 

.21 

22.00 

16.35 

•65 

—  .01 

12 

Canum  Venat. 

F. 

9 

12 

49 

3-76 

—  .01 

—0.18 

0.00 

.19 

3-57 

57-88 

.69 

-b.oi 

Polaris,  S.  P.  . 

F. 

5 

13 

10 

42. 10 

+■  -41 

+  3-53 

-4-93 

•  99 

41  .  II 

35-27 

.84 

S 

Bootis. 

F. 

9 

15 

19 

42. 16 

—  .01 

—0. 18 

0.00 

.19 

41.97 

36.24 

.73 

-•03 

a 

Cor.  Borealis. 

F. 

9 

15 

29 

18.31 

—  0.01 

-0.15 

—0.03 

—0. 19 

18. 12 

12.33 

-5-79 

+  .03 

April  26 

T 

Leonis 

F. 

5 

II 

21 

23.19 

—  0.02 

—  0.07 

—0.04 

-0.13 

23.06 

15.90 

-7.16 

-•03 

V 

Leonis 

F. 

9 

30 

25.83 

.02 

.06 

.04 

.  12 

25.71 

18.43 

.28 

+  .08 

0 

Virginis  . 

F. 

9 

II 

58 

43-43 

.02 

.07 

-  .04 

•  13 

43.30 

36.13 

•17 

-.05 

12 

Canum  Venat. 

F. 

9 

12 

50 

5.20 

•03 

.  10 

.00 

•  13 

5-07 

57.87 

.20 

-•05 

e 

Virginis  . 

Ha. 

9 

13 

3 

21.70 

—  .02 

—0.06 

—0.05 

-  -13 

21-57 

14.41 

.  l6 

+  .06 

Polaris,  S.  P.  . 

F. 

5 

10 

42.68 

+  .83 

+  2.02 

—2.30 

+  -55 

43-23 

35-95 

.28 

S 

Virginis  . 

F. 

9 

28 

12.88 

—  .02 

—  0.06 

0.04 

—  .  12 

12.76 

5-42 

•  34 

+  .06 

V 

Bootis. 

Ha. 

9 

13 

48 

38.14 

.02 

.08 

•03 

•  13 

38.01 

30.91 

.  10 

-■03 

a 

Serpentis  . 

F. 

9 

15 

38 

0.63 

.02 

.07 

,04 

•  13 

0.50 

53-15 

•  35 

—  .02 

e 

Serpentis  . 

Ha. 

9 

15 

44 

28.79 

—  0.02 

—  0.07 

—  0.04 

—0.13 

28.66 

21.44 

—  7.22 

+  .01 

April  30 

0 

Virginis  . 

Ha. 

9 

1 1 

58 

45-19 

—  0.02 

—  0.  10 

—0.08 

—  0.20 

44-99 

36.11 

-S.8S 

—  .OI 

V 

Virginis  . 

Ha. 

9 

12 

13 

25-43 

.02 

.09 

.  10 

.21 

25.22 

16.32 

.90 

+  .01 

p 

Corvi  . 

Ha. 

9 

12 

27 

44.11 

—  .02 

—0.06 

0.15 

0.23 

43-88 

34-93 

•95 

+  .05 

Polaris,  S.  P.  . 

Ha. 

5 

13 

10 

48.10 

+  .83 

+2.77 

5-26 

1.66 

46.44 

37-53 

.91 

a 

Virginis  . 

Ha. 

9 

18 

31.12 

—  .02 

—  0.01 

0.  12 

0.21 

30.91 

22.06 

.85 

—  .06 

? 

Virginis  . 

Ha. 

9 

28 

14-54 

.02 

.09 

.  10 

.21 

14-33 

5-43 

.90 

—  .01 

V 

Bootis. 

Ha. 

9 

13 

48 

40.00 

.02 

.  II 

.06 

.19 

39.81 

30.93 

.88 

-•03 

a 

Bootis. 

Ha. 

9 

14 

9 

54-37 

—  0.02 

—  0.  II 

—0.06 

—0. 19 

54.18 

45.20 

—8.98 

+  .06 

WASHINGTON  AND  ST.  LOUlS. 


13 

Each  of  the  quantities  in  the  column  “Observed  Clock  Corr .”  is  equal  to 

«  —  \_T'  +  Aa  +  Bb  +  Cc] 

which,  for  brevity,  we  will  represent  by  n.  Then  each  star  observed  furnishes  an 
equation  of  condition  of  the  form 

o  =  —  n  +  A  T0  -f-  R  (  I  —  Tf)  -(-  v 

and  from  all  the  equations  thus  obtained  on  any  given  night  the  values  of  AT,  and  II 
for  that  night  have  been  found  by  the  method  of  least  squares.  Assuming  T0  —  1  ih  o"1 
by  the  face  of  the  Kessels  clock,  the  equations  of  condition,  normal  equations,  and 
resulting  values  of  AT,  and  II,  for  each  night,  are  as  follows: 


Washington, 

Equations  of  Condition. 

0  —  +  :-9S  +  Al,  +  0.35  11 
O  m  — b  1 .90  - b  A  I g  — f—  o.  50  lb 
o  — (-  2 .00  — h  A  J  0  ~ h  o.  7 1  R 
o  =  +  i-95  +  AT0  +  0.98  11 
o  —  +  2.00  +  AT,  -f  1.22  It 
o  —  +  1  -97  H~  Al0  -f-  2.05  11 


April  12,  1870. 

Normal  Equations. 

o  —  +  1 1.80  +  6.00  A T0  -f-  5.81  11 
0  —  +  1 J-45  +  5-^ 1  A 1 0  +  7.53  It 
Hence 

S.  s. 

AT,  —  —  1.954  ±  0.010 
II  — —  0.0133 


Washington,  1 

Equations  of  Condition. 

o  =  +  5.62  +  AT,"  +  0.51  R 
o  =  +  5.69  +  AT,"  +  0.71  R 
o  =  +  5.61  -f-  ATf  -J-  0.98  R 
o  —  +  5.65  +  A 10  -f-  1.22  11 
o  —  5.69  -f-  AT,  -(-  1.82  R 

°  —  +  5-73  +  AT''  -j-  4.33  R 
o  =  +  5-79  +  AT 0 '  +  4.49  R 

Washington,  I 
Equations  c 

o  —  +  7-I(^  +  AT,"  -f-  0.36  R 
o  —  +  7.28  +  AT,"  +  0.51  R 
o  —  -j-  7- 1 7  ~h  A 1,  -(-  0.98  R 
o  —  +  7-2°  "T  A 1,  -(-  1.83  II 
o  —  +  7.16  +  AT,  +2.06  R 


’RIL  23,  1870. 

Normal  Equations. 

o  —  +  39- 78  +  7.00  AT,"  +  14.06  It 
o  =r  +  80.46  +  14.06  AT,"  +  45.43  R 
Hence 

AT,"  —  —  5.615  ±  0.008 
R  —  —  0.0335 


PRIL  26,  1870. 
r'  Condition. 

o  —  d~  7-34  +  JTo"  +  2.47  R 
o  =r  +  7.10  +  AT,  +2.81  R 
o  —  +  7-35  +  *Tf  +  4.63  R 
o  —  +  7-2  2  +  AT,  +  4.74  R 


DIFFERENCE  OF  LONGITUDE, 


H 


Normal  Equations. 

8. 

°  =  +  43-5°  +  6.00  4T0"  -J-  o.oo  BT0  -f-  10.78  11 

°  =  +  21.48+  0.00  BTf  +  3.00  JT0  +  9.61  n 

0  =  +  I47-58  +  10.78  JT0"  +  9.61  A T0  +  66.84  It 

Hence 

4  T0"  =  —  7. 1 76  +  0.0 1 6 
0  =  —  7.013  +  0.019 
B  —  —  0.0423 


Washington, 
Equations  of  Condition. 

o  =  +  8.88  +  JT,  +  0.98  B 
o  =:  +  8.90  +  JT0  +  1.22  B 
0  —  +  8.95  +  4Tq  +  1.46  It 
0  —  +  8.85  +  4T0  +  2.31  B 
0  =  +  8.90  +  4T0  +  2.47  B 
o  z=  +  8.88  +  BT0  +  2.81  It 
o  =  +  8.98  +  4T0  +  3. 1 6  B 


April  30,  1870. 

Normal  Equations. 

8. 

o  —  +  62.34+  7.00  +  14.4!  y> 

0  —  +  1 28-38  +  14.41  4T0  -\-  33.90  It 

Hence 

4T0  —  —  8.880  +  0.01 1 
B  —  —  0.01 2 1 


As-will  be  shown  farther  on,  Mr.  Frisby  observes  the  transit  of  an  equatorial  star 
os.  1 2 1  later  than  T,  and  therefore  we  have 


4Tn  —  J  T0"  +  os.  1 2 1 

Hence,  on  April  23, 

4T0  =  —  5s-6i5 +os.i2i -- 5s.494  +  o«.ooS 

On  April  26,  Mr.  Frisby’s  observations  give 

4T,  —  —  7s.  1 76  +  os.  1 2 1  —  —  71055  +  os.oi6 

and  my  own  give 

4B0  =  —  7s-Q!3  +  os.oi9 

Taking  the  mean,  we  find 


4 B0  —  7 -°34  i  os.oi4 

Collecting  our  results,  we  have  the  expressions  given  in  Table  III  for  the  correc¬ 
tions  which  must  be  applied  to  the  time  indicated  by  the  face  of  the  Kessels  clock,  in 
order  to  reduce  it  to  sidereal  time  determined  by  myself  at  the  meridian  of  the  transit 
circle.  T  is  the  time  indicated  by  the  clock  at  the  instant  for  which  the  correction  is 
required,  and  the  quantities  after  the  sign  +  are  approximately  the  probable  .errors. 


Table  III. — Corrections  to. the  Kessels  Clock. 


Date. 

Correction.  , 

April  12 

s-  s.  h.  s. 

—  1.954  —  0.0133  {T1  —  ir. 00)  ±  0.010 

23 

—  5-494  —  0.0335  {T'  —  11. 00)  ±  0.008 

26 

—  7.034  —  0.0423  (T'  —  11. 00)  ±  0.014 

30 

—  S.8S0  —  0.0121  (T'  —  11. 00)  ±  0.011 

WASHINGTON  AND  ST.  LOUIS. 


15 


St.  Louis  Observations. — The  observations  for  time  at  St.  Louis  were  made  by  Pro¬ 
fessor  William  Limbeck,  and  are  given  in  Table  IV.  The  first  column  contains  the 
date.  The  column  “Lamp”  gives  the  position  of  the  axis  of  the  transit  instrument;  L. 
signifying  that  the  lamp  .was  to  the  east,  W.  that  it  was  to  the  west.  The  column 
“No.  of  Wires ”  gives  the  number  of  wires  over  which  the  transit  of  the  star  was 
observed.  The  field  of  view  of  the  instrument  contained  nine  vertical  wires,  separated 
by  intervals  of  about  15  seconds  of  time,  but  as  a  rule  only  the  middle  seven  wires 
were  used,  and  all  observations  were  made  by  the  eye  and  ear  method.  The  column 
11  Star”  does  not  require  any  explanation.  The  column  “Time  of  Transit  over  Mean 
of  Wires ”  contains  the  time  of  transit  over  an  imaginary  wire  situated  at  the  mean 
of  the  standard  set  of  seven  wires.  For  stars  not  observed  over  all  the  wires  of  that 
set  the  time  of  transit  over  the  mean  wire  has  been  deduced  from  the  observed  times 
of  transit  by  the  application  of  the  necessary  corrections.  The  column  “ b ”  contains 
the  observed  values* of  the  level  constant,  each  of  them  being  derived  from  two  readings 
of  the  spirit-level,  one  made  with  it  in  the  direct,  the  other  with  it  in  the  reversed  posi¬ 
tion.  The  level  is  of  the  striding  form,  and  each  division  of  its  scale  is  equal  to  os.c>9. 
The  columns  “Bb”  and’“Cc”  contain  the  corrections  for  level  and  collimation.  The 
column  “r”  contains  the  correction  for  rate  of  the  chronometer.  The  column  “Corr. 
Transit'''  contains  the  sum  of  the  quantities  111  the  columns  “Time  of  Transit  over  Mean 
of  Wires ,”  “Bbf  “Co”  and  “r.”  The  column  “Adopt'd  Bight  Ascension”  contains  the 
adopted  apparent  right  ascensions  of  the  stars  observed.  The  column  “Obs'd  Chron 
Correction "  contains  the  difference  between  the  “Corr.  Transit ”  and  the  “Adopt'd  Bight 
Ascension.''  The  column  “v”  contains  the  difference  between  the  observed  and  adopted 
chronometer  correction;  or,  in  other  words,  the  error  of  observation. 

Throughout  the  whole  series  of  time  determinations  the  adopted  value  of  B  is 
— os.o86;  and  the  adopted  value  of  c  is  -f-  os.2q  for  lamp  west.  The  latter  constant  was 
obtained  from  transits  of  circumpolar  stars,  each  observation  being  made  over  one-half 
the  wires  with  the  lamp  west,  and  over  the  other  half  with  lamp  east. 


i6 


DIFFERENCE  OF  LONGITUDE, 


Table  IV. — Transits  of  Stars  observed  at  St.  Louis  to  determine  the  Corrections  to  the 
Sidereal  Chronometer  Kcssels  and  Dent  No.  1287. 


Date. 

Lamp. 

No.  of  Wires. 

Star. 

Time  of 
Transit  over 
Mean 
of  Wires. 

b 

Bb 

Cc 

r 

Corr.  Transit. 

Adopt’d  Right 
Ascension. 

Obs’d  Chron. 

Correction. 

V 

1870. 
April  12 

E. 

7 

£ 

Hydras  . 

h.  m.  s. 

8  33  U-99 

s. 

—0.09 

s. 

—0.08 

s, 

—  0.24 

s. 

-0.05 

m.  s. 

33  14-62 

m.  s. 

39  53.6o 

m.  s. 

+  6  38.98 

s. 

—  .02 

E. 

7 

L 

Ursae  Maj.  . 

43  40.78 

•  13 

•  19 

•  36 

.07 

43  40.16 

50  17.91 

37-75 

+  .04 

E. 

7 

K 

Cancri  . 

8  54  4-Oi 

•  19 

0.17 

0.24 

.08 

54  3.52 

0  42.51 

38.99 

-■13 

E. 

4 

I 

Draconis  . 

9  11  54-42 

1 .09 

1 . 70 

.11 

11  51.52 

18  22.27 

30.75 

+  .06 

E. 

7 

a 

Hydra:  . 

14  33-6o 

-0.15 

—0.24 

.  12 

14  33.09 

21  12.38 

39-29 

—  .02 

E. 

5 

p 

Cephei,  S.P. 

20  I4.2I 

.23 

+  .22 

+  .70 

.  12 

20  15.01 

26  57.21 

42.20 

+  .14 

W. 

7 

t 

Leonis  . 

31  50.04 

•  25 

+  .27 

.26 

•13 

31  49.90 

38  28.54 

38.64 

-.05 

W. 

7 

ti 

Leonis  . 

38  43-89 

•  17 

•  19 

•  27 

•15 

38  43.82 

45  22.41 

38.59 

-.oS 

W. 

4 

a 

Leonis  . 

9  54  48.57 

.09 

.09 

.24 

•17 

54  48.55 

1  27.37 

38.82 

+  .02 

W. 

7 

P 

Librae  . 

15  3  23.16 

.20 

.14 

.24 

.01 

3  23.25 

10  1.90 

38.65 

+  .02 

W. 

7 

s 

Bootis  . 

11  58.53 

.24 

•  30 

•03 

11  58.56 

19  36.07 

37-51 

+  .09 

W. 

3 

y 2 

Ursae  Min.  . 

14  25.43 

.19 

■  52 

•79 

•03 

14  25.67 

21  0.50 

34-83 

+  .10 

W. 

5 

a 

Coronae  Bor. 

22  34.24 

•  17 

.20 

.27 

•04 

22  34.27 

29  12.16 

37-89 

+  .02 

W. 

7 

a 

Serpentis  . 

31  14-53 

•  15 

+  .24 

•05 

31  14.57 

37  52.94 

38.37 

—  .02 

E. 

7 

£ 

Serpentis  . 

37  43-21 

•  15 

—  0.24 

.06 

37  42.76 

44  21.21 

38.45 

—  .06 

E. 

5 

UrsaeMin.  . 

42  19.07 

.68 

1. 17 

.06 

42  17.16 

48  50.29 

33-13 

-.09 

E. 

6 

yS1 

Scorpii  . 

15  5i  15-33 

—0. 18 

—  0. 10 

-0.25 

—0.07 

51  14.91 

57  53.86 

+  6  38.95 

—  .06 

April  23 

E. 

5 

I 

Draconis  . 

9-  11  53-62 

+0. 10 

+0.52 

-1.70 

-0.03 

11  52.41 

18  20.82 

+  6  28.41 

+  .29 

E. 

7 

a 

Hydrae  . 

14  46.81 

+  .05 

—  0.24 

•03 

14  46.59 

21  12.22 

25.63 

—  .06 

E. 

6 

p 

Cephei,  S.P. 

20  33.02 

+  .01 

-  .04 

+  .70 

■03 

20  33.65 

26  57.90 

24.25 

+  .2S 

E. 

7 

£ 

Leonis  . 

32  2.9O 

.00 

—  .  26 

•05 

32  2.59 

38  28. 3s 

25-79 

+  .05 

E. 

7 

Leonis  . 

38  56.97 

—  .11 

—  .  12 

•27 

.06 

38  56.52 

45  22.25 

25.73 

+  •13 

E. 

7 

a 

Leonis  . 

9  55  1.96 

.  16 

•  14 

0.24 

.08 

55  1.50 

1  27.23 

25-73 

.OO 

E. 

7 

9 

Draconis  . 

10  17  34.12 

.18 

.60 

—  1.02 

.  12 

17  32.38 

24  O.I4 

27.76 

-•31 

W. 

7 

/ 

Leonis  . 

36  0.31 

•  25 

.22 

+0.24 

.  -14 

36  0.19 

42  25.99 

25.80 

—  .oS 

W. 

7 

a 

Ursae  Maj.  . 

10  49  15.53 

.20 

.40 

•  52 

.  16 

49  15.49 

55  42.23 

26.74 

—  .26 

W. 

7 

ti 

Leonis  . 

n  0  46.54 

.18 

•  25 

•17 

0  46.44 

7  12.25 

25.81 

.00 

W. 

6 

d 

Crateris 

6  26.13 

•  17 

.11 

.24 

.is 

6  26.08 

12  51-45 

25-37 

+.16 

w. 

7 

A 

Draconis  . 

17  14-56 

•  15 

.38 

•  70 

.20 

17  14.68 

23  41-50 

26.82 

+.05 

w. 

7 

P 

Leonis  . 

36  0.89 

•  14 

■  24 

.22 

36  0.77 

42  26.51 

25-74 

+ .02 

w. 

7 

y 

Ursae  Maj.  . 

40  33-90 

•  15 

.24 

O.4I 

•23 

40  33-84 

47  0.29 

26.45 

—  .20 

w. 

4 

4 

Draconis  . 

11  59  40.77 

-0.15 

-0.57 

+1. 19 

—0. 26 

59  4I-I3 

6  8.85 

+  6  27.72 

—  .06 

April  26 

w. 

4 

I 

Draconis  . 

9  11  5691 

0.00 

0.00 

+  1.70 

—0.02 

11  58.59 

18  20.42 

+6  21.83 

+.65 

w. 

7 

a 

Hydrae  . 

14  52.59 

.00 

+0.24 

.03 

14  52.80 

21  12. iS 

I9.3S 

.00 

w. 

7 

p 

Cephei,  S.P. 

20  40.66 

-  .07 

+  .07 

-  -70 

•03 

20  40.00 

26  58.12 

iS.  12 

+•13 ! 

w. 

7 

£ 

Leonis  . 

32  8.46 

•  05 

-  .05 

+  .26 

•05 

32  8.62 

38  28.33 

19.71 

-.07! 

w. 

7 

Leonis  . 

39  2.47 

.08 

.09 

.27 

.06 

39  2.59 

45  22.20 

19.61 

+■05 ! 

w. 

7 

a 

Leonis  . 

9  55  7-49 

.02 

.02 

•24 

.08 

55  7-63 

1  27.17 

19-54 

.00 

w. 

6 

r1 

Leonis  . 

10  6  28.33 

—  .01 

—  .OI 

0.25 

.  10 

6  29.07 

12  4S.50 

19.49 

+.11 

w. 

5 

9 

Draconis  . 

17  36.82 

+  .04 

+  -13 

+  1.02 

.  12 

17  37.S5 

23  59-94 

22.09 

—  .S6 

E. 

4 

a 

Ursae  Maj.  . 

10  49  22.66 

0.00 

0.00 

—0. 52  I 

1 

—0.16 

49  21. 98 

55  42.15 

+  6  20.17 

+ .  20 

1 

WASHINGTON  AND  ST.  LOUIS. 


l7 


Table  IV. — Transits  of  Stars  observed  at  St.  Louis ,  &c. — Continued. 


Date. 

Lamp. 

No.  of  Wires. 

.Star. 

Time  of 
Transit  ovei 
Mean 
of  Wires. 

b 

Bb 

Cc 

r 

I  Corr.  Transit. 

|  Adopt’d  Right 
Ascension. 

Obs’d  Chron. 
Correction. 

V 

1S70. 

h.  m.  s. 

s. 

s. 

s. 

s. 

m.  s. 

m.  s. 

m.  s. 

s. 

April'26 

E. 

5 

4 

Lconis  . 

11  0  53.07 

—0.05 

—0.05 

—0.25 

-0.17 

0  52.60 

7  12.23 

+  6  19.63 

—  .  02 

• 

E. 

5 

X 

Draconis  . 

17  21-79 

.06 

•  15 

.70 

.  20 

17  20.74 

23  41.38 

20.64 

.OO 

E. 

7 

p 

Lconis  . 

36  7-57 

■  ■ 

.09 

.25 

.  22 

36  7-0i 

42  26.49 

19.48 

4-.0S 

E. 

7 

7 

Ursx  Maj.  . 

40  40.93 

.09 

.15 

•41 

•23 

40  40.14 

47  0.25 

20.  1 1 

-.07 

E. 

7 

0 

Virginis  . 

52  17-26 

.12 

.  10 

0.24 

.24 

52  16.68 

58  36.13 

19-45 

+ .  06 

E. 

6 

4 

Draconis  . 

11  59  4S.90 

1  .12 

.46 

r.19 

—  .26 

59  46.99 

6  8.69 

21.70 

[  — .  l6 

E. 

7 

a2 

Librae  . 

14  37  24.30 

.  . 

.06 

0.24 

4-  .02 

37  24.02 

43  42.74 

18.72 

'  4-  .02 

E. 

7 

p 

Urspc  Min.  . 

44  51-66 

.  . 

•  31 

.91 

4-  .01 

44  50.45 

51  10.95 

20. 50 

j  —.OI 

E. 

5 

p 

Bootis  . 

14  50  45-57 

.10 

•  13 

•31 

.00 

50  45-13 

57  4-39 

19.26 

+  .01 

E. 

7 

p 

Librae  . 

15  3  43-73 

■  15 

.  10 

•24 

—  .01 

3  43-38 

10  2. II 

18.73 

+  .07 

E. 

7 

s 

Bootis  . 

13  17-57 

.20 

•  25 

•30 

.02 

13  17.00 

19  36.27 

19.27 

-.04 

. 

E. 

7 

a 

Coronac  Bor. 

22  53.82 

.21 

•  23 

.27 

.04 

22  53.28 

29  12. 3s 

19. 10 

.OO 

E. 

7 

a 

Serpcntis  . 

31  34. So 

.19 

• 1 7 

-0.24 

•05 

3i  34-34 

37  53.17 

is. S3 

1  +  .09 

W. 

5 

c 

Ursx  Min.  . 

42  29.61 

.21 

•79 

+  1.17 

.06 

42  29.93 

48  50.97 

21.04 

+  .04 

w. 

7 

E 

Coronx  Bor. 

45  54-58 

•23 

0.27 

.07 

45  54-55 

52  13.70 

19-15 

-•03 

w. 

4 

d1 

Scorpii  . 

5i  35-39 

•  17 

.  10 

•25 

.08 

5i  35.46 

57  54.15 

18.69 

+  .01 

w. 

5 

Groom.  2320 

15  59  4i.i6 

•  . 

.28 

.65 

.09 

59  41-44 

6  1.40 

19.96 

4-  .06 

w. 

7 

r 

Ilcrculis 

16  9  32.17 

.07 

.  10 

•  35 

.  11 

9  32.31 

15  5i.7o 

19-39 

—  .  02 

w. 

5 

7 

Draconis  . 

15  56.34 

.06 

.  12 

•  5i 

.  12 

15  56.61 

22  16.44 

19.83 

-.10 

w. 

7 

? 

Ophiuchi  . 

23  42.36 

•03 

.24 

.  12 

23  42.45 

30  1.27 

18.82 

-.03 

w. 

6 

V 

Ilcrculis 

16  36  8.33 

—  0.04 

-0.05 

+0.31 

—0.13 

36  8 . 64 

38  27.76 

+6  19.30 

.OO 

April  30 

w. 

2 

I 

Draconis  . 

9  12  6.15 

0.00 

+  1.70 

—0.02 

12  7.83 

18  19.87 

+  6  12.04 

—  .62 

w. 

7 

a 

Hydra  . 

14  59-36 

.00 

+0.24 

•03 

14  59-57 

21  12.12 

12-55 

+  .07 

w. 

5 

/? 

Cephei,  S.  P. 

20  46.08 

—  .02 

+  .02 

-  -70 

•03 

20  45.37 

26  58.36 

12.99 

4-  .06 

w. 

7 

£ 

Lconis  . 

32  15.66 

.08 

-  .0.3 

4-  .  26 

•05 

32  15.78 

38  2S.27 

12.49 

+  .03 

w. 

7 

r 

Lconis  . 

39  9.56 

.08 

.09 

4-  .27 

.06 

39  9-68 

45  22.14 

12.46 

+  .05 

w. 

3 

79 

Drac.,  S.  P. 

45  2.00 

+  .11 

-  .83 

.07 

45  1. 21 

51  14-50 

13.29 

-•15 

w. 

7  • 

a 

Lconis  . 

9  55  14-47 

.  II 

—  .  10 

4-  .24  1 

.08 

55  14.53 

1  27.14 

12.61 

-•05 

w. 

4 

32 

Ursx  Maj.  . 

10  2  21 . Si 

.08 

.17 

0.59 

.09 

2  22.14 

8  34-35 

12.21 

+  .01 

w. 

7 

9 

Draconis  . 

17  46.74 

—  .02 

-  .07 

1 .02  1 

.  12 

17  47-57 

23  59-64 

12.07 

—  .  l6 

w. 

7 

1 

Lconis  . 

36  13.16 

.00 

4-0.24 

.14 

36  13.26 

42  25.91 

12.65 

-.09 

w. 

4 

L 

Cephei,  S.  P. 

38  49.86 

.00 

.00 

-  .58 

.15 

38  49- r3 

45  2.49 

13.36 

—  .40 

w. 

7 

a 

U rsx  Maj. . 

10  49  29.29 

4-  .04 

-f-  .  oS 

4-  .52 

.  16 

49  29.73 

55  42.01 

12.28 

—  .  IO 

7 

d 

Lconis  . 

11  0  59.94 

+  .02 

+  .02 

-  .25 

.17 

0  59-54 

7  12.18 

12.64 

—  .11 

E. 

5 

d 

Crateris 

6  39.22 

-  .03 

.  .24 

.iS 

6  38.77 

12  51-37 

12.60 

+  .04 

E. 

6 

T 

Lconis  . 

i5  3-83 

; 

.06 

.24 

.19 

15  3-34 

21  15.87 

12.53 

+  .05 

E. 

4 

"k 

Draconis  . 

17  30-35 

—  .11 

.28 

.70 

.  20 

17  29.17 

23  41.22 

12.05 

4-  .08 

E. 

7 

P 

Lconis  . 

36  14.61 

.18 

.25 

.22 

36  13.96 

42  26.46 

12.50 

4-. 05 

E. 

7 

7 

Ursx  Maj. . 

40  48.93 

•23 

.38 

.41 1 

•  23 

40  47.91 

47  0.17 

12.26 

4-. 10 

E. 

7 

0 

Virginis 

52  24.36 

•29 

0.26 

0.24 

•  25 

52  23.61 

58  36.11 

12.50 

-b.07 

E. 

5 

4 

Draconis  . 

11  59  59.70 

1 . 10 

I  .  19  ! 

.26 

59  57.15 

6  8.45 

n.30 

-f-  .  48 

E. 

7 

V 

Virginis 

12  7  4-55 

—0.30 

0.23 

0.24 

.  26 

7  3-82 

13  16.31 

12.49 

4-. 10 

E. 

6 

K. 

Draconis  . 

12  21  47.81 

—0.76 

—0.72 

—  O.29 

21  64.04 

27  57.78 

+6  11.74 

4-. 14 

3 — w  s 


DIFFERENCE  OF  LONGITUDE, 


I  8 

Each  of  the  quantities  in  the  column  “  Obs'd  Citron.  Correction ”  is  equal  to 

«  -  | \r  Hb  B  ( T  -  To)  +  Bb  +  6 V] 

wliich,  for  brevity,  may  be  represented  by  n.  Then  we  have 

O  m  n  — (—  A  / o  - b  Ad  — |—  v 

But  as  throughout  this  series  of  observations  n  is  very  large,  we  write 

AT0  —  GfSG 

and  the  equation  just  given  becomes 

o  —  —  n  Q  SG  Aa  +  v 

in  which  the  absolute  term,  —  n  +  G,  may  be  made  sufficiently  small  by  choosing  a 
suitable  value  of  G.  Each  star  observed  furnishes  an  equation  of  condition  of  this  form, 
and  from  all  the  equations  so  obtained  on  any  given  night  the  values  of  SG  and  a  for 
that  night  have  been  found  by  the  method  of  least  squares. 

The  adopted  values  of  T0  and  G  for  each  night,  together  with  the  equations  of  con¬ 
dition,  normal  equations,  and  resulting  values  of  SO  and  a,  are  as  follows: 

St.  Louis,  April  12,  1870. 


Equations  of  Condition ; 

T,  =  7h  53“  22s 
o  —  —  8.98  -j-  SG  -f-  0.529  a 
o  —  —  7-75  +  —  0.274  a 

o  —  —  8.99  -f-  SG  -j-  0.462  a 
o  —  —  0.75  -f-  SG  —  4.850  a 
o  —  —  9.29  -f-  8G  -f-  0.734  a 


1st  Group,  8U  to  1  o'1. 

G  —  6m  30s.ooo 

s. 

o  =  -  1 2.20  +  SG  4-  2.760  a 
o  —  —  8.64  +  SG  -f-  0.267  a 
o  —  —  8.59  -T  -f-  0.232  a 
or=:  —  8.82  -)-  SG  -f-  0.449  a 


Normal  Equations. 


o  —  —  74.01  -f  9.00  SG  -f-  0.34  a 
0  —  52.10  +  0.34  SG  -f  32.56  a 

Hence 


60  =  -fo  8.163 

«  =  +  o  1. 515 

41'0  —  +  6  38.163  d=  os.oi9 


Equations  of  Condition ; 

T0  =  1411  53m  22s 

o  =  —  8.65  +  SG  -)-  0.746  a 
o  —  —  7.5 1  -p  +  0.0 1 7  a 
o  =  —  4.83  -f  SG  —  1.820  a 
o  —  —  7.89  +  SG  -j-  0.223  a 


2  d  Group,  1511  to  i6u. 

G  —  -f-  6m  3os.ooo 

s. 

°  =  — 8.37  +  -f-  0.530  a 

o  —  '  8.45  +  SG  4-  0.557  a 

0  =  —  3-x3  +  ~  3-I2o  a 

o  —  —  8.95  +  SG  -f-  0.899  a 


WASHINGTON  AND  ST.  LOUIS. 


19 


Normal  Equations. 

8. 

o  —  —  57.78  +  8.00  (5(9 —  1.970 
o  =  —  6.97—  1.97  69  +  15.05  a 

Hence 

•  m.  s. 

<59  —  4-0  7.582 
0  =  4-0  1.455 
^Tq  —  4"  6  37.582  +  os.oi8 

St.  Louis,  April  23,  1870. 

Equations  of  Condition. 


T0  =  8h  53“  34s 
o~  -  8.41  4-  <59  —  4.850  a 
o  —  5.634- <594-0.7340 

O  =  —  4.25  4-  <5 9  4-  2.760  0 
o  =  —  5.79  4-  <59  4-  0.267  a 
o  =  —  5.73  4-  <594-0.232  o 
o  =  — 5. 73  4- <59  4- 0.4490 
o  =  —  7.76  4-  (59  —  2.600  o 
o  =  —  5.80  4-  (59  4-  0.469  o 


9  =  -L  6m  20s. OOO 
8. 

o  =  —  6.74  4-  (59  —  0.875  a 
o  =  —  5.81  —{-  (5 9  4-  0.320  a 
o  =  —  5.37  4-  <59  4-  0.820  o 
o  =  —  6.82  -f-  <59  —  1.530  o 
o  =  —  5.74  (59  4-  0.41 1  a 

o  =  —  6.45  -|-  <59  —  0.468  o 
o  =  —  7.72  -|-  <59  —  3. 160  o 


Normal  Equations. 


o  =  — 93.75  4- 15.00  <59  —  7.020 
0  =  4-72.07—  7.02  <59  4-  53.24  o 

Hence 

Ill.  S. 

69  =  +  o  4988 
o  =  —  o  0.564 
—  4-  6  25.988  +  o\o33 

St.  Louis,  April  26,  1870. 


Equations  of  Condition; 

T0  =  8"  53“  40s 

o  =  — 3.83  4-69  —  4.8500 
o  —  —  1-38  +  694-0.7340 
o  =  —  o.  1 2  +  69  4-  2. 760  a 
o  —  —  1.7 1  +  69  +  0.267  a 
o  ~  —  1.6 1  +  69  +  0.232  o 
o  —  1.54  +  (59  +  0.449  o 

o  =  —  1.49  +  <50  + 0.33 1  a 

o  —  —  4.09  +  69  —  2.600  o 


1st  Group,  9h  to  1211. 

9  =  4-6“  1 8s.ooo 

s. 

0  =  —  2. 17  +  69  —  0.875  a 
o  =  —  1.63  +  69  +  0.320  o 
o  =  —  2.64  +  69  —  1.530  a 
o  =  —  1.48  +  69  -]-  0.41 1  o 
0  =  —  2. 11 +  69  —  0.468  a 
0  =  —  1.45  +  694-0.493  o 
o  =  —  3.70  +  69  —  3. 160  o 


20 


DIFFERENCE  OF  LONGITUDE, 


Normal  Equations. 

8. 

o  =  — 30.95  +  15.00  <50—  7.49  a 
0  =  4-42.64—  7.49  <50  +  52.70  a 

Hence 

m.  s. 

<50  =  +  o  1.786 
«  =  -o  0.555 
4rl0  =  4-6  19.786  4=  os.o57 


Equations  of  Condition 

T0—  14'“  5  3 m  4i  s 

o  =  —  0.72  4-  <50  4-  0.838  a 
o  =  —  2.50  4-  <50  —  2. 1 30  a 
o  =  —  1.26  -{-  <50  —  0.052  a 
o  =  —  0.73  -f-  <50  -f  0.746  a 

0  =  —  1 . 2  7  4-  <5  0  4~  0-0 1 7  a 

0  =  —  1 . 1  o  -j-  <50  -f-  o. 2 23  « 
o  =  —  0.83  4-  <50  +  0.530  a 
o  =  —  3.04  -(-  <50  —  3-120  a 


;  2d  Group ,  1411  to  1  71'. 

0  =  -f-  6m  1 8s.ooo 

8. 

0  =  —  1.15  4“  <50  4“  0.222  a 
o  =  —  0.69  4-  <50  4*  0.899  a 
o  =  —  1.96  4-  <50  —  1.330  a 
o  =  —  1.39  4-  <50  —  0.189  a 
o  =  —  1.83  4-  (50  —  0.836  a 
o  =  —  0.82  4-  (50  4-  0.764  a 
o  =  —  1.30  4 -  <50  —  0.0 1 1  a 


Normal  Equations. 


o  =  —  20.59  4-  1 5-oo  (50  —  3.43  a 
0  =  4-15.92—  3.43  <50  4-  19.81  a 

Hence 

m.  s. 

(50  =  4-0  1.237 
a  —  —  o  0.590 
4T0  =  +  6  19.237  4=  01009 

St.  Louis,  April  30,  1870. 


Equations  of  Condition. 


T0  =  8”  53m  48s 
8. 

o  =  —  0.04  -f  (50  —  4.850  a 
o  =  —  0.55  -f  60  +  0.734  a 
o  =  —  0.99  -j-  <50  4-  2.760  a 
o  =  —  0.49  4-  <50  4-  O-2  67  a 
o  =  —  0.46  4-  <50  -f-  0.232  a 
o  =  —  1.29  4-  <50  4~  3.190  a 
o  =  —  0.61  4-  <50  4-  0-449  a 

0  =  —  0.21  -f  (50  —  1 . 1 1  o  a 
o  =  —  0.07  4-  <50  —  2.600  a 
o  =  —  0.65  -j-  <50  4-  0.469  a 
o  =  —  1.36  -j-  <50  4-  2.340  a 


0  =  4-6™  1 2  s.  000 

o  =  —  0.28  4-  (50  —  0.875  a 
o  =  —  0.64  4-  <50  4-  0.320  a 
o  =  —  0.60  <50  4-  0.820  a 

o  =  — 0.53  4-  <504-0.574(1 
o  =  —  0.05  4-  <50  —  1.530  a 
o  =  —  0.50  <50  4-  0-41 1  a 
o  =  —  0.26  <50  —  0.468  a 
o  =  —  0.50  +  <50  4-  0.493  « 
0  =  4-  0.70  <50  —  3.160  a 

o  =  —  0.49  -j-  <50  -}-  0.622  a 

0=4-0264 -  <50  —  1.580  a 


H-H- 


WASHINGTON  AND  ST.  LOUIS. 


2  I 


Normal  Equations. 

S. 

o  —  —  9.61  -f-  22.00  dO —  2.49  a 
0=1—14.56-  2.49  se  +  73.59  a 

Hence 

111.  s. 

60  —  +  o  0.461 
a  —  -f  o  o.  2 1 4 
AT0  —  A  6  1 2.46 1  A  os-03 1 

These  values  of  AT0  apply  to  the  sidereal  chronometer  Kessels  and  Dent  No.  1 287. 
But  in  the  exchange  of  longitude  signals  the  mean-time  chronometer  Dent  No.  2748 
was  employed,  and  its  corrections  were  determined  every  evening,  both  before  carry¬ 
ing  it  to,  and  after  bringing  it  back  from,  the  telegraph-office,  by  comparing  it  with 
No.  1287  by  the  method  of  coincidence  of  beats.  The  comparisons  on  each  night, 
together  with  the  resulting  expressions  for  the  corrections  of  No.  2748,  are  as- follows: 

April  12. — When  No.  1287  indicated  yh  5 3 1,1  12s  its  correction  was  -f-  6m  38s.  163  A: 
os.oi9,  and  when  it  indicated  1 41'  53"'  22s  its  correction  was  +  6m  373.582  A:  os.oi8.  It 
was  therefore  gaining  os.o83Q  per  hour. 


Chronometer  Comparisons. 


Before  going  to  Telegraph-Office. 

After  returning  from  Telegraph-Office. 

No.  1287.  No.  2748. 

No.  12S7.  No.  2748. 

h.  m.  s.  h.  m.  s. 

10  11  14.0=  8  53  36.0 

14  20.5  =  56  42.0 

17  25.0  =  59  46.0 

h.  m.  s.  h.  m.  s. 

14  39  32.0  “  13  21  10. 0 

42  39.0  =  24  1C.5 

"4  s'  43-0  =  27  20.0 

Hence,  if  T  is  the  sidereal  time  at  the  meridian  of  the  transit  instrument,  and  T' 
the  time  indicated  by  No.  2748,  we  have 

T  —  T'  A  k1  24ra  3bs.575  +  9s-783  (T'  —  i’ih)  Az  o3.oiS 
April  23. — When  No.  1287  indicated  8U  53”1  34s  its  correction  was  -f-  6m  253.988 
01033;  and  when  it  indicated  8h  53”1  40s  on  April  26,  its  correction  was  A  6m  i9s-786 
os.057.  It  was  therefore  gaining  o3.o86i  per  hour. 


Chronometer  Comparisons. 


Before  going  to  Telegraph-Office. 

After  returning  from  Telegraph-Office. 

No.  1287.  ■  No.  2748. 

No.  1287.  No.  2748. 

h.  m.  s.  h.  m.  s. 

12  4  24.0  =10  3  25.0 

7  29.5  =  6  30.0 

10  35.0  =  9  35.0 

h.  m.  s.  li.  m.  s. 

15  1  33.0  =13  0  5.0 

4  35-0  =  3  6.5 

6  39.0  =  6  10. 0 

T—T'  A  211  7m  33s-922  +  9s-765  (t'  ~~  1  ih)  zb  o.s033 


Hence 


22 


DIFFERENCE  OF  LONGITUDE, 


April  26. — When  No.  1287  indicated  8h  53"1  40s  its  correction  was  +  6m  i98.786 
Az  o8.057;  and  when  it  indicated  14'*  53“  41s  its  correction  was  -f-  6ra  i98.237  Az  o\oog. 
It  was  therefore  gaining  os.09i5  per  hour. 

Chronometer  Comparisons. 


Before  going  to  Telegraph-Office, 

After  returning  from  Telegraph-Office. 

No.  1287.  No.  2748. 

No.  1287. 

No.  2748. 

h.  m.  s.  h.  m.  s. 

h.  m.  s. 

h.  m.  s. 

12  9  31.0  =  9  56  45.0 

14  22  33.0  = 

12  9  25.O 

12  40.0  =  9  59  53.5 

25  39-°  = 

12  30.5 

15  42.0  =10  2  55.0 

28  39.0  — 

15  30.0 

Hence 

T  —  T'  -)-  2’1  19111  i5s.869  -f-  9-s862  (T1  —  1  ih)  Az  0^030 
April  30. — When  No.  1287  indicated  81'  53111  40s,  on  April  26,  its  correction  was 
-f-  6m  1 9s. 786  Az  os.057;  and  when  it  indicated  8h  53™  48s,  on  April  30,  its  coiTection 
was  +  6m  i2s.46i  Az  os.03i.  It  was  therefore  gaining  os.o763  per  hour. 


Chronometer  Comparisons. 


Before  going  to  Telegraph-Office. 

After  returning  from  Telegraph-Office. 

No.  1287.  No.  274S. 

I 

No.  1287.  No.  2748. 

h.  m.  s.  h,  m.  s. 

12  27  10.5  =  9  58  40.0 

30  16.0  =10  1  45.0 

33  2T.5  =  4  50.0 

h.  m.  s.  h.  m.  s. 

14  56  25.0  12  27  30.0 

14  59  30.0  =■  30  34.5 

15  2  34.0  =  33  33.0 

Hence 

T  —T‘  A-  211  34111  5  2s.  701  +  9s-Soi  ( T /  —  1  iu)  Az  os.o3 1 
Collecting  our  results,  we  have  the  expressions  given  in  Table  V  for  the  correc¬ 
tions  which  must  be  applied  to  the  time  indicated  by  the  face  of  the  mean-time  chro¬ 
nometer  Dent  No.  2748  in  order  to  reduce  it  to  sidereal  time  at  the  meridian  of  the 
transit  instrument.  T'  is  the  time  indicated  by  the  chronometer  at  the  instant  for  which 
the  correction  is  required,  and  the  quantities  after  the  sign  Az  are  approximately  the 
probable  errors. 

Table  V. — Corrections  to  the  Chronometer  Bent  No.  2748. 


Date. 

Correction. 

h.  m.  s.  s.  h.  s. 

April  12 

+  1  24  36. 575  +  9. 7S3  {T1  —  11. 00)  ±  0.018 

23 

+  2  7  33.922  +  9.765  {T’  —  it. 00)  ±  0.033 

26 

+  2  19  15.869  -I-  9.S62  ( T 1  —  ix. 00)  ±  0.030 

3° 

+  2  34  52.701  +  9.801  ( T '  —  11. 00)  ±  0.031 

WASHINGTON  AND  ST.  LOUIS. 


2.3 


VI.— PERSONAL  EQUATION. 

In  the  beginning  of  August,  1870,  Professor  Eimbeck  came  to  Washington,  bring¬ 
ing  with  him  his  sidereal  chronometer  Ivessels  and  Dent  No.  1287,  and  his  portable 
transit  instrument  C.  S.  No.  7.  The  latter  was  soon  mounted  on  the  collimator  pier  to 
the  north  of  the  transit  circle  and  our  relative  personal  equation  was  determined  in  the 
following  manner:  Professor  Eimbeck  and  I  made  observations  for  time  simultaneouslv, 
he  using  his  own  chronometer  and  portable  transit  instrument,  and  I  using  the  transit  cir¬ 
cle,  the  Ivessels  clock,  and  chronograph.  As  far  as  possible  we  both  employed  the  same 
stars.  At  the  conclusion  of  each  night’s  work  he  took  my  observing-key,  and,  by  tap¬ 
ping  upon  it  in  coincidence  with  the  beats  of  his  chronometer,  recorded  upon  the  chro¬ 
nograph  connected  with  the  Ivessels  clock  a  series  of  signals  similar  to  those  which  he 
sent  from  St.  Louis  when  making  telegraphic  comparisons  of  time  for  difference  of 
longitude.  The  correction  necessary  to  reduce  the  local  time  determined  by  him  to 
that  determined  by  myself  thus  became  known,  and  as  his  instrument  and  mine  were 
in  precisely  the  same  meridian,  this  correction  is  evidently  the  required  personal  equa¬ 
tion. 

The  observations  for  time  made  at  Washington  with  the  transit  circle  are  given 
in  Table  VI,  the  arrangement,  of  which  is  similar  to  that  of  Table  II.  The  values  of 
the  constants  employed  during  each  night  are  as  follows: 


Date. 

C 

b 

a 

August  5 

s. 

+  O.O4 

s. 

—  0.21 

s. 

—  0.02 

8 

+  .05 

-  .24 

—  .01 

12 

+  .05 

-  -23 

-  -03 

15 

0.00 

—  0.27 

—  0.24 

24 


DIFFERENCE  OF  LONGITUDE, 


Table  VI. — Transits  of  Stars  Observed  at  Washington  with  the  Transit  Circle  to  deter¬ 
mine  the  Corrections  to  the  Kessels  Sidereal  Clock 


Date. 

Star. 

Observer. 

No.  of  Wires. 

Time  of 

Transit  over 
Mean  of  Wires 

Cc 

Bb 

1 

A  a 

1  Correction  for 
Instrument. 

Corr.  Transit. 

Adopt’d  Right 
Ascension. 

Obs’d  Clock 
Correction. 

1870. 

h.  m.  s. 

s. 

s. 

s. 

s. 

i  s. 

s. 

s. 

S.  1 

Aug.  5 

K 

Ophiuchi  . 

Ha. 

9 

16  52  15.60 

+0.04 

— 0. 19 

—0  01 

—0. 16 

15-44 

32.49 

-42.95 

—  .  IO 

d 

Herculis  . 

Ha. 

9 

16  57  33-H 

•  °5 

.25 

.00 

.20 

32.91 

49-75 

43- 16 

+  .10 

C 

Sagittarii  . 

IL, 

9 

18  6  44.63 

.04 

0.  II 

—  .02 

O.O9 

44-5.4 

1.49 

43-05 

.OO 

(l 

U rsx  Minoris 

Ha. 

5’ 

15  13.60 

t-  .67 

+2.38 

+  -25 

-r. 46 

12.14 

2S.55 

43-59 

5 1  Ccphei,  S.  P.  . 

Ha. 

5 

iS  39  8.75 

-  -83 

+  2.56 

-  -33 

+  1.40 

10.15 

27-94 

42.21 

7 

Aquilx 

Ha. 

9 

19  40  50.04 

+  .04 

—  0. 19 

.01 

—0. 16 

49.88 

6.91 

42.97 

—  .OS 

ft 

Aquilx 

;  Ha. 

9 

49  41.06 

0.04 

0. 18 

—  .01 

0.15 

40.91 

57.82 

43-09 

+  .05 

X 

Ursx  Minoris 

Ha. 

4 

19  55  55-55 

2.  T  I 

7.14 

+  .81 

4.22 

51-33 

12.58 

38.75 

U'2 

Capricorni 

Ha. 

9 

ro 

O 

CO 

O 

-t-0.04 

—0.13 

—  0.02 

—  0.  II 

OI 

U» 

CO 

52.72 

—43.06 

-j-  .02 

Aug.  8 

n 

Herculis  . 

Ha. 

9 

16  39  11.42 

+0.06 

-0.31 

0.00 

—0.25 

II. 17 

27.72 

-43-45 

-•03 

H 

Ophiuchi  . 

Ila. 

9 

16  52  16. 10 

•  05 

0.21 

.00 

.  16 

15-94 

32.45 

43-49 

+  .01 

E 

Ursa;  Minoris 

Ha. 

5 

17  0  9.59 

•  37 

1.29 

+  .05 

.87 

8.72 

25.49 

43-23 

a1 

Herculis  . 

Ha. 

9 

9  2S.43 

•  05 

0.23 

.OO 

.18 

28.25 

44.81 

43-44 

-.04 

44  Ophiuchi  . 

Ila. 

9 

17  19  11.53 

•  05 

0.  12 

—  .or 

0.08 

11.45 

27.94 

43-51 

+  .03 

6 

Ursx  Minoris 

S. 

7 

18  15  11.70 

+0.84 

-2.72 

+  .12 

-1.76 

9-94 

27-54 

42.40 

5i 

Cephei,  S.  P.- . 

S: 

5 

39  8.50 

—  1.03 

+2.93 

—  -17 

+  I-73 

10.23 

29.17 

41.06 

0 

Lyrx  . 

S. 

9 

18  46  2.64 

+0.06 

—  O.29 

.00 

-0.23 

2.41 

18.87 

43-54 

+  .02 

K. 

Aquilx 

Ila. 

9 

19  30  39.67 

•  05 

•  17 

—  .01 

•13 

39-54 

56.02 

43-52 

+  .04 

y 

Aquilx 

Ha. 

9 

40  50.52 

•  05 

.21 

.00 

.  l6 

50.36 

6.91 

43-45 

-.°3 

0 

Aquilx 

S. 

9 

49  4I-48 

0.05 

0.20 

—  .01 

0. 16 

41.32 

57- S2 

43-50 

—  .02 

X 

Ursx  Minoris 

S. 

4 

19  55  58.82 

+2.64 

-8.16 

+0.41 

-5-  n 

53-71 

IO.65 

— 43-o6 

Aug.  12 

Polaris,  S.  P.  . 

S. 

5 

13  12  38.60 

—  2.07 

+  5- 80 

—0.98 

+  2-75 

4.1  •  35 

56.82 

-44-53 

a 

Virginis  . 

F. 

9 

19  5.91 

+0.05 

-0.15 

.02 

—  O.  12 

5-79 

21.23 

44-56 

+  .01 

Virginis  . 

F. 

9 

13  28  49.31 

•  05 

.  18 

.02 

•  15 

49. 16 

4-63 

44-53 

—  .02 

£ 

Bootis. 

F. 

9 

14  40  3.89 

.06 

•  25 

.01 

.  20 

3-69 

I9-I5 

44-54 

.OI 

a2 

Librae  . 

. 

F. 

9 

44  26.97 

•  05 

.14 

-  -03 

.  12 

26.85 

42.31 

44-54 

—  .OI 

0 

Bootis. 

F. 

9 

14  57  48.23 

.07 

•  30 

.00 

•  23 

48.00 

3  37 

44-63 

.  oS 

0 

Librx  . 

F. 

9 

15  10  46.53 

•  05 

.  l6 

—  .02 

•  13 

46.40 

1.87 

44-53 

—  .02 

a 1 

Herculis  . 

Ha. 

9 

17  9  29.46 

•  05 

2° 

.01 

.iS 

29.28 

44-76 

44-52 

+.05 

a 

Ophiuchi  . 

Ha. 

9 

29  40.32 

•05 

.21 

•OI 

•  17 

40.15 

55.68 

44-47 

.00 

iu 

Herculis  . 

Ha. 

9 

17  42  8.61 

.06 

.26 

.OI 

.21 

8.40 

23-93 

44-47 

.00 

c 

Sagittarii  . 

Ha. 

9 

iS  6  46.07 

.05 

O.  12 

-  -03 

O.  10 

45-97 

1.44 

44-53 

+ .06 

6 

Ursx  Minoris 

Ha. 

5 

15  11.65 

.84 

2,60 

+  -37 

i-39 

10.21 

26.22 

43-99 

I 

Aquilx 

Ha. 

9 

28  54.62 

•05 

0. 16 

—  .02 

0.13 

54-49 

10.00  • 

44-49 

+.02 

a 

Lyrx  . 

Ha. 

9 

33  18.79 

+.0.06 

—  O.29 

.OO 

—0.23 

18.56 

34-20 

44-36 

— .  11 

51 

Cephei,  S.  P.  . 

S. 

5 

j8  39  13.22 

-1.05 

+2.81 

-  -50 

+  1.27 

14.49 

30.77 

43-72 

6 

Aquilx 

S. 

9 

19  19  43.36 

+0.05 

—  O.I9' 

.02 

—0. 16 

43-20 

58.73 

44-47 

-.oS 

K 

Aquilx 

S. 

9 

30  40.76 

•05 

.  16 

.02 

•  13 

40.63 

56.02 

44.61 

+ .06 

7 

Aquilx 

s. 

9 

40  51.61 

0.05 

0.21 

—  0.01 

0.17 

51-44 

6.90 

44-54 

—  .01 

X 

Ursx  Minoris 

s. 

5 

19  55  56.26 

2.64 

7.82 

+  1.22 

3-96 

52.30 

7.82 

44 -4S 

£ 

Delphini  . 

s. 

9 

20  27  47.08 

0.05 

0.21 

—  0.01 

O.  17 

46.91 

2.36 

44-55 

.00 

I 

Pegasi 

s. 

9 

21  .16  51.49 

•05 

•23 

.01 

.19 

5I-30 

6.79 

44-51 

-.04 

0 

Aquarii 

s. 

9 

21  25.29.87 

+0.05 

— 0. 16 

—  0.02 

—  0. 13 

29.74 

45-i6 

-44- 5S 

+  .03 

WASHINGTON  AND  ST.  LOUIS. 


25 


Table  VI. — Transits  of  Stars  Observed  at  Washington ,  dec. — Continued. 


Date. 

Star. 

Observer. 

No.  of  Wires. 

Time  of 
Transit  over 
Mean  of  Wires. 

Cc 

Bb 

A  a 

!  Correction  for 
Instrument. 

Corr.  Transit. 

Adopt’d  Right 
Ascension. 

Obs’d  Clock 

Correction. 

V 

1870. 

h.  m. 

s. 

s. 

s. 

s. 

s. 

s. 

s. 

s. 

s. 

Aug.15 

a 

Ophiuchi  . 

E. 

9 

17  29 

41-47 

0.00 

—0.25 

—0. 11 

—  0.36 

41 .  II 

55-63 

-45-48 

+  .03 

u 

Herculis  . 

Ha. 

9 

42 

9-52 

.00 

•  30 

•05 

■35 

9.17 

23.88 

45-29 

—  .06 

y 2 

Sagittarii  . 

E. 

9 

m 

CO 

15-44 

.00 

.  II 

.26 

•  37 

15.07 

29.67 

45-40 

-.04 

C 

Sagittarii  . 

Ha. 

9 

is  6 

47.19 

.00 

0.15 

—0.22 

•  37 

46.82 

1.41 

45-41 

+  .07 

6 

Ursae  Minoris 

H.&E. 

II 

15 

IO.QI 

.00 

3.06 

+3.00 

.06 

vn 

00 

6 

25-30 

45-55 

I 

Aquilae 

Ha. 

9 

28 

55-69 

.00 

0. 19 

—0. 18 

■  37 

55-32 

9.98 

45-34 

.00 

a 

Lyrae  . 

E. 

9 

33 

19.88 

.00 

-0.35 

0.00 

•  35 

19-53 

34-15 

45-3S 

-.05 

51 

Cephei,  S.  P.. 

H.&E. 

i  1 

39 

18.31 

.00 

+  3.29 

-4.01 

•  72 

17-59 

31.82 

45-77 

p 

Lyrae  . 

Ha. 

9 

18  46 

4.49 

.00 

—0.32 

0.03 

•  35 

4.14 

18.79 

45-35 

+  .02 

? 

Aquilae 

E. 

9 

ig  0 

13.90 

.00 

•  25 

.  11 

•36 

13-54 

2S  .09 

45-45 

.02 

(5 

Aquilae 

Ha. 

9 

19 

44.41 

.00 

.  22 

.14 

•36 

44-05 

58.71 

45-34 

.OI 

n 

Aquilae 

E. 

9 

30 

41-83 

.00 

.19 

.17 

•  36 

41.47 

56.01 

45.46 

+  .04 

y 

Aquilae 

Ha. 

a 

40 

52-53 

.00 

.24 

.  12 

•  36 

52.17 

6.89 

45.28 

-.04 

a 

Aquilae 

E. 

9 

19  45 

14-37 

0.00 

—  O.  24 

—  0. 12 

—0.36 

T4.0I 

28.60 

-45-41 

—  .01 

Assuming  T0  —  i6b  om  by  face  of  the  Kessels  clock,  and  0  —  —  4os.ooo,  the 
equations  of  condition,  normal  equations,  and  resulting  values  of  69  and  R  for  each 
night  are  as  follows  : 


Washington,  August  5,  1870. 


Equations  of  Condition. 


Normal  Equations. 


o 

o 

o 

o 

o 

o 


—  T  2.95  +  60  -(-  0.87  R 

—  -}-  3.16  -j-  <5 <9  -f-  0.96  R 

—  +  3-05  +  60  +  2. 1 1  R 

—  +  2.97  +  69  +  3.68  R 

—  +  3-° 9  +  d#  +  3-^3  A 

—  +  3.06  +  69  -f-  4. 1 9  R 


o  =  + 18.28  +  6.00  69  +  1 5.64  R 
o  ~  +  47.62  +  15.64  69  +  51.90  R 
Hence  s. 

69  —  —  3.046 
R  —  +  0.0004 
RT0  —  —  43.046  +  os.o2  2 


Washington,  August  8,  1870. 

On  this  evening  observations  were  made  by  two  persons,  and  therefore  two  values 
of  RT0  have  been  introduced  in  the  equations. 


4 — w  s 


26 


DIFFERENCE  OF  LONGITUDE, 


Equations  of  Condition. 

8. 

Or=  + 3.45  +  (50+  o  +  0.65  72 
0  —  H“  3-49  89  +  o  +  0.87  H 

0  —  +  3-44  +  89  +  o  +  1. 1 6  It 
0  =  +  3-5 1  f  89  f-  o  +1.32/1! 

°  =  +  3-54  +  0  +  89"' f-  2.77  It 
o  =  +  3.52  +  (50+  o  +3.51/2 
o  —  +  3-45  +  89  +  o  +3.68/2 
0=r  +  3.50+  O  +  69"'  +  3.83  It 

Normal  Equations. 

o  =  +  20.86  +  6.00  39  +  0.00  39"'  +11.19  72 
o  —  +  7-°4  “l-  0.00  39  +  2.00  89"'  +  6.60  72 
o  =  +  62.16  +  1 1. 19  39  +  6.60  39"'  +  52.47  11 

Hence 

89  —  3.475 

89'"  —  —  3-518 
72  —  —  0.001 1  s 
4T0  =  —  43.475  +  0.010 
JT0'"  =  —  43-518  +  0.014 

Washington,  August  12,  1870. 

On  this  evening  observations  were  made  by  three  persons,  and  therefore  three 
values  of  the  clock  correction  have  been  introduced  in  the  equations. 

Equations  of  Condition.. 


0  =  +  4.56  +  39" 

+  0  + 

0 

-  2.68/2 

°  =  +  4-53  +  89" 

+  0  + 

0 

—  2.52  72 

°-  +  4-54  +  89" 

+  0  + 

0 

—  i-33  72 

0  —  +  4-54  +  89" 

+  0  + 

0 

—  1.26/2 

0  =  +  4-63  +  80" 

+  0  + 

0 

—  1.03  72 

0  =  +  4-53  +  89" 

+  0  + 

0 

-  0.82  72 

0=1  +  4.52  + 

0 

+  89  + 

0 

+  1 . 1 6  72 

0  —  +  4-47  + 

0 

+  39  + 

0 

+  1.49  72 

0  —  +  4-47  + 

0 

+  39  + 

0 

+  1 . 70  72 

0  —  +  4-53  + 

0 

+  89  + 

0 

+  2.1 1  72 

0  —  +  4-49  + 

0 

+  (50  + 

0 

+  2.48  72 

0=1  +  4.36  + 

0 

+  (50  + 

0 

+  2.5  6  72 

0  —  +  4-47  + 

0 

+  oE  89"' 

+  3-33  72 

O  nz  — (—  4.61 

0 

+  of- 39"' 

+  3-5i  72 

0  —  +  4-54  + 

0 

+  of- 89'" 

+  3- 68  72 

°  =  +  4-55  + 

0 

+  of- 89"' 

+  4.46  72 

0  —  +  4-51  + 

0 

+  of- 69'" 

+  5.28  72 

0  =  +  4-58  + 

0 

+  0  +  39'" 

+  5.42  72 

WASHINGTON  AND  ST.  LOUIS.  *  27 


Not 

mat  Equations. 

O  2= 

+ 

27-33  + 

6.00  59" 

+ 

0.00 

59  + 

0.00 

59"‘ 

'  — 

9-64 

R 

O  2= 

+ 

26.84 

0.00  59" 

+ 

6.00 

59  + 

0.00 

59'" 

'  + 

11.50 

R 

O  2= 

+ 

27.26 

0.00  59" 

+ 

0.00 

<50  + 

6.00 

59"' 

'  + 

25.68 

R 

O  2= 

+ 

124.18  — 

9.64  59" 

+ 

11.50 

59  + 

25.68 

59"' 

'  + 

156.33 

R 

Tice 

59" 

— 

8. 

-4-554 

59 

— 

-  4-474 

59'" 

— 

-4-545 

R 

— 

+  0.0005 

S. 

4T0" 

2= 

-  44-554 

±  0.0 1  I 

JT0 

— 

-  44-474 

±  0.0 1 7 

JT'" 

— 

—  44-545 

±  0.014 

Washington, 

August  15, 

,  1870. 

On  this  evening  observations  were  made  by  two  persons,  and  therefore  two  values 
of  the  clock  correction  have  been  introduced  in  the  equations. 

Equations  of  Condition. 

S. 

o  =  +  5.48  +  59'  +  o  +  1.50  It 
0=2  +  5.29+  0  +  59  +1.70  It 

o  =  +  5.40  +  59'  +  0+1.97  It 
o  — +  5.41+  o  +  d<9  +  2.1 1  12 

o  =  +  5.34  +  o  +  <50+  2.48  E 

o  —  +  5-38  +  8d'  +  o  +  2.56  12 

0=2  +  5.35  +  o  +  <50  +  2.77  R 

o  =  +  5.45  +  59'  +  o  +  3.00  R 

0=2  +  5.34+  o  +  60  +  3.33  R 

o  =2  +  5.46  +  59'  +  o  +  3.51  R 

o  —  +  5.28  +  o  +  59  +  3.68  R 

02=  +  5.41  +  59'  +  o  +  3.75  R 

Normal  Equations. 

o  =  +  32.58+  6.00  5 9'  +  0.00  59  +  16.29  12 

o  =  +  32.01+  0.00  59'  +  6.00  <50  +  16.67  12 

o  =  +  1 74.1 1  +  16.29  +  16.07  6#  +  93.86  R 

59'  =2—  5.465 
59  ——  5.370 
R  —  +  0.0129  s. 

4 T0'  —  —  45465  ±'0.010 
4T„  2=  — 45.370  +  0.013 


Hence 


28 


DIFFERENCE  OF  LONGITUDE, 


The  observations  for  time  made  at  Washington  by  Professor  Eimbeck  with  the 
poi table  tiansit  instinment  (  .  S.  iso.  7  are  given  in  I  able  VII,  the  arrangement  of 
which  is  similar  to  that  of  Table  IV.  These  observations  were  reduced  by*Professor 

Keith  of  the  Coast  Survey,  who  adopted,  throughout  the  whole  series,  U  — _ os.032, 

and  c  —  +  os-547  with  lamp  west.  The  latter  constant  was  determined  from  measures 
made  with  the  right-ascension  micrometer  of  the  transit  circle;  that  instrument  being- 
used  as  a  collimator  to  the  portable  transit  instrument.  As  already  explained,  some  of 
the  right  ascensions  employed  by  Professor  Keith  differed  slightly  from  those  used  at 
this  Observatory,  and  on  that  account  a  few  small  changes  have  been  made  in  his 
reductions  by  Mr.  Frisby  and  myself. 


WASHINGTON  AND  ST.  LOUIS. 


29 


Table  VII. — Transits  of  Stars  Observed  at  Washington  bg  Professor  William  Eimbeck  with 
the  Portable  Transit  Instrument  C.  S.  No.  7,  to  determine  the  Corrections  to  the  Sidereal 
Chronometer  Kessels  and  Dent  No.  1287. 


Date. 

d, 

S 

No.  of  Wires. 

Star. 

Time  of 

1  Transit  over 
Mean 
of  Wires. 

b 

Bb 

Cc 

r 

Corr.  Transit. 

Adop’d  Right 

Ascension. 

Obs’d  Chron. 

Correction. 

V 

1870. 

h. 

m.  s. 

s. 

s. 

s. 

s. 

111. 

S. 

m.  s. 

m.  s. 

s. 

Aug.  5 

E. 

3 

£ 

Ursae  Min. . 

l6 

4  13-32 

+0.09 

4-0.48 

— 

4.08 

4-0.03 

4 

9-75 

59  25-97 

+55 16.22 

+0.76 

E. 

7 

44  Ophiuchi  . 

23  10.53 

.06 

■  03 

0.60 

.02 

23 

9.98 

18  27.97 

17.99 

.02 

E. 

6 

C J 

Draconis  . 

42  29. 12 

•  07 

•  17 

1-52 

4-  '.01 

42 

27.78 

37  45-31 

17.53 

+ 

.08 

E. 

7 

y 

Draconis  . 

l6 

58  20.28 

•  04 

.06 

0.89 

.00 

58 

19-45 

53  37-33 

17.88 

- 

•  65 

E. 

5 

S 

Sagittarii  . 

17 

10  43.62 

0.04 

0.59 

.00 

10 

43-07 

6  1.50 

18.43 

- 

•  43 

E. 

4 

J 

Ursae  Min.  . 

19  21.20 

.  1 1 

4-1.25 

- 

9-30 

.00 

19 

13-15 

14  28.44 

15.29 

+ 

•  44 

E. 

5 

51 

Cephei,  S.P. 

17 

42  57.81 

.  1 1 

-i-34 

4- 1 1 . 40 

—  .02 

43 

7.85 

38  28.06 

20.21 

+ 

.44 

E. 

5 

j 

Aquilae  . 

r3 

23  41.14 

4-0.09 

- 

0-55 

.04 

23 

40.64 

18  58.74 

18.10 

- 

.  l6 

E. 

7 

li 

Aquilae  . 

34  38.39 

.  1 1 

.oS 

•55 

.04 

34 

37-88 

29  56.03 

18.15 

.18 

E. 

6 

y 

Aquilae. 

44  49-43 

.  10 

•56 

•  05 

44 

48.92 

40  6.92 

18.00 

•  07 

E. 

7 

a 

Aquilae  . 

18 

49  11.02 

.  10 

•  55 

•  05 

49 

10.52 

44  28.61 

18.09 

.  l6 

E.? 

7 

a * 

Capricorni . 

19 

15  35-19 

+  0.  II 

4-0.07 

— 

0-57 

—0.06 

15 

34-63 

IO  52.72 

+55 18.09 

0.  1 1 

Aug.  8 

E. 

7 

/31 

Scorpii  . 

15 

2  38.51 

4-0.01 

— 

0.58 

4-0.06 

2 

a 

38.00 

57  54-34 

+55 16.34 

+0. 10 

E. 

6 

r 

Herculis  . 

20  36.03 

+0.02 

.03 

.80 

•  05 

20 

35-31 

15  51-24 

15-93 

- 

.08 

E. 

7 

r 

S 

Ophiuchi  . 

34  45-89 

4-  .03 

.02 

-56 

•04 

34 

45-39 

30  1.69 

16.30 

+ 

.08 

E. 

7 

7 

Herculis  . 

43  12.50 

4-  .02 

•7i 

.04 

43 

11.85 

38  27.72 

15-87 

.07 

E. 

7 

K 

Ophiuchi  . 

15 

56  16.83 

.00 

•56 

.04 

56 

16.31 

5i  32.45 

16. 14 

.09 

E. 

6 

Herculis 

I C) 

1  34-50 

•  i 

-  -03 

0.66 

•  03 

I 

33-84 

56  49-70 

15-86 

.14 

E. 

4 

£ 

Ursae  Min. . 

4  17-18 

-  -07 

•38 

4-05 

•  03 

4 

12.79 

59  25.50 

12.71 

+ 

.46 

E. 

7 

a1 

Herculis  . 

12  29.16 

.oS 

.08 

0. 56 

•  03 

12 

28.55 

8  44.81 

16.26 

- 

.08 

E. 

7 

44  Ophiuchi  . 

23  11.96 

-  .04 

- 

0.60 

•  03 

23 

n-35 

18  27.94 

16.59 

.11 

E. 

3 

Gr’m.g66,S.P. 

27  0.51 

4-  .11 

4- 

2. 10 

.02 

27 

2.74 

22  21.15 

18.41 

•  54 

E. 

6 

a 

Ophiuchi  . 

33  40.08 

.06 

-  -05 

- 

0. 56 

.02 

33 

39-49 

28  55-72 

16.23 

- 

.04 

E. 

6 

0) 

Draconis  . 

42  31-92 

.  11 

.26 

- 

1.52 

4-  .01 

42 

30.15 

37  45 • 16 

15.01 

+0.18 

W. 

7 

y 

Draconis  . 

16 

58  20.79 

.09 

•  14 

4- 

0.88 

.00 

58 

21-53 

53  37-25 

15-72 

- 

I  .  72 

w. 

7 

C 

Sagittarii  . 

17 

10  44.36 

•03 

0.59 

.00 

10 

44-92 

6  1.48 

16.56 

- 

O.  II 

w. 

3 

<5 

Ursae  Min. . 

19  10.24 

.01 

—  .11 

4- 

9.24 

.00 

19 

19-37 

14  27.43 

8.04 

+  1.10 

w. 

4 

5i 

Cephei,  S.P. 

17 

43  15-74 

-  .04 

-H  •  4^ 

- 

H-34 

-  .01 

43 

4.87 

38  29.28 

24.41 

+  0.70 

w. 

7 

c 

Aquilae  . 

18 

4  11.40 

4-  .01 

.01 

4- 

0.  56 

•03 

4 

11.94 

59  28.14 

16.20 

- 

.01 

w. 

7 

d 

Sagittarii  . 

14  46.86 

.01 

•  58 

•  03 

14 

47.42 

10  3-95 

16.53 

+ 

.10 

w. 

7 

6 

Aquilae  . 

23  41 . 88 

•03 

.02 

•55 

.04 

23 

42.41 

18  58.74 

16-33 

- 

.06 

w. 

7 

Aquilae  . 

34  39-23 

.01 

•  55 

.04 

34 

39-75 

29  56.03 

16.28 

+ 

.  12 

w. 

7 

y 

Aquilae  . 

44  50.15 

.02 

•  56 

•  05 

44 

50.68 

40  6.91 

16.23 

- 

.02 

w. 

7 

a 

Aquilae  . 

18 

49  H-77 

4-0.02 

4-0.02 

4- 

0-55 

—0.06 

49 

12.28 

44  28.61 

+  55  16.33 

— 

O.  10 

Aug.  12 

E. 

7 

6 

Ophiuchi  . 

T5 

12  20.33 

—0.04 

-0.03 

— 

0.55 

4-0.06 

12 

19.81 

7  33-40 

+  55  13-59 

+  0. 12 

E. 

7 

V 

Draconis  . 

27  3-49 

—  .01 

—  .02 

I  .  l6 

•  05 

27 

2.36 

22  15.14 

12.78 

.  l6 

E. 

7 

Ophiuchi  . 

15 

34  48.44 

.00 

0.56 

■  05 

34 

47-93 

30  1. 61 

13-68 

0.17 

Ef 

3 

£ 

Ursae  Min. . 

l6 

4  19-65 

+  .05 

4-05 

•03 

59 

15-68 

59  24.86 

9.18 

+  1.04 

E. 

7 

a1 

Herculis  . 

l6 

13  31 .96 

4-0.03 

4-0.03 

— 

0.56 

4-0.03 

13 

34-46 

8  44-75 

+  55  13-29 

+0.03 

/ 


DIFFERENCE  OF  LONGITUDE, 


O 


Table  VII. — Transits  of  Stars  Observed  at  Washington,  dee. — Continued. 


Date. 

Lamp. 

No.  of  Wires.  | 

Star. 

Time  of 
Transit  Over 
Mean  of 
Wires. 

b 

Bb 

Cc 

r 

Corr.  Transit. 

Adop’d  Right 
Ascension. 

Obs’d  Chron. 

Correction. 

V 

1870. 

h.  m.  s. 

s. 

s. 

S. 

s. 

m.  s. 

m.  s. 

m.  s. 

s. 

Aug.  12 

E. 

7 

44  Ophiuchi  . 

16  23  14.74 

+  0.02 

+0.01 

—  0.61 

+0.03 

23  14-17 

18  27.89 

+55 13-72 

—0.09 

E. 

7 

a  Ophiuchi  . 

33  42.86 

+  .03 

+  .03 

0.56 

.02 

33  42.35 

28  55.68 

13-33 

+  .01 

E. 

6 

(j  Draconis  .. 

42  34.22 

-  .04 

—  .  10 

1.52 

+  .01 

42  32.61 

37  44-96 

12.35 

—0.04 

E. 

7 

y  Draconis  . 

16  58  25.01 

—  .02 

-  -03 

0.88 

.00 

58  24.10 

53  37-15 

13-05 

—  1.98 

E. 

7 

/1'  Sagittarii  . 

17  10  48.43 

•  • 

+  .01 

0.59 

.00 

10  47.85 

6  i-44 

13-59 

+  0.01 

E. 

3 

S  Ursae  Min.  . 

19  29.99 

+  .05 

+  -57 

-  9.24 

.00 

19  21.32 

14  26.11 

4-79 

+  1.30 

E. 

2 

51  Cephei,S.P. 

42  56.32 

+  .01 

—  .  12 

+  H-34 

—  .02 

43  7-52 

38  30.78 

23.26 

-0.75 

E. 

2 

51  Cephei,S.P. 

17  43  20.54 

—  .06 

+  -73 

-H-34 

.02 

43  9-91 

38  30.78 

20.87 

+  1.64 

W. 

7 

£  Aquilae. 

iS  4  14.27 

—  .02 

—  .02 

+  0.56 

•03 

4  I4-78 

59  28.11 

13-33 

—0.08 

W. 

7 

(5  Aquilae  . 

23  44.78 

.OO 

.OO 

■55 

•03 

23  45-30 

18  58.72 

13-42 

.01 

W. 

7 

it  Aquilae  . 

34  42.00 

.OO 

.OO 

•55 

.04 

34  42.51 

29  56.02 

I3-5I 

.02 

W, 

7 

y  Aquilae  . 

44  52.83 

.OO 

.56 

.05 

44  53-34 

40  6.90 

13-56 

.20 

W. 

7 

a  Aquilae  . 

49  14.50 

—  .OI 

•55 

•05 

49  15.00 

44  28.60 

13.60 

•  23 

W. 

7 

P  Aquilae  . 

18  53  43- S3 

.OI 

•55 

•05 

53  44-32 

48  57-8i 

13-49 

.  IO, 

W. 

7 

e  Delphini  . 

19  31  48.44 

—  .02 

.02 

•  56 

.07 

31  48.91 

27  2.36 

13-45 

.  10 

W. 

6 

a  Cygni  . 

19  41  48.88 

—  0.02 

—0.03 

+  0.77 

—0.08 

41  49.54 

37  2.62 

+  55  13-oS 

—0.07 

Aug.  15 

W. 

7 

r)  Herculis 

15  43  16.34 

—  0.01 

—  0.01 

+  0.71 

+0.04 

43  17-oS 

3S  27.58 

+  55  10.50 

—  0.  10 

W. 

7 

k  Ophiuchi  . 

15  56  21.03 

+  -03 

0.56 

•03 

56  21.65 

5i  32.35 

10.70 

-  .09 

w. 

3 

e  Ursae  Min.. 

16  4  12.34 

+  .05 

.26 

4-05 

•03 

4  16.68 

59  24-35 

7.67 

+  .28 

w. 

7 

44  Ophiuchi  . 

23  16.26 

.04 

0.60 

•03 

23  16.93 

18  27.85 

10.92 

+  .05 

w. 

7 

a  Ophiuchi  . 

33  44-iS 

.14 

.  12 

0.56 

.02 

33  44-88 

28  55.61 

10.73 

-  .oS 

w. 

7 

w  Draconis  . 

42  33-24 

.09 

.22 

1.52 

+  .02 

42  35-00 

37  44-79 

9-79 

0.07 

w. 

7 

y  Draconis  . 

16  58  25.80 

.08 

.  12 

•0.88 

,.00 

58  26.80 

53  37-07 

10.27 

2.00 

w. 

7 

ft1  Sagittarii  . 

17  10  49.97 

.05 

•59 

.00 

10  50.61 

6  1 .41 

10.80 

0.14 

w. 

7 

7  Serpentis  . 

19  25.41 

.  II 

+0.08 

+  0.55 

.00 

19  26.04 

14  36.87 

10.83 

-  -05 

w. 

4 

51  Cephei.S.P. 

43  26.07 

.  12 

—  1.46 

—  11-34 

—  .01 

43  13-26 

38  31-84 

18.58 

+0.27 

E. 

3 

51  Cephei,S.P. 

17  43  1.48 

.20 

—2.44 

+  H-34 

.02 

43  10.36 

38  31-84 

21. 4S 

1.06 

E. 

7 

f  Aquilae  . 

18  4  18.09 

•  25 

+0.23 

—  0.56 

.02 

4  17-74 

59  28.09 

10.35 

0.0S 

E. 

7 

d  Sagittarii  . 

14  53-79 

•  25 

.14 

.58 

•03 

14  53-32 

10  3.93 

10.61 

.08 

E. 

7 

(5  Aquilae  . 

23  48.66 

•  19 

•  55. 

•03 

23  48.27 

18  58.71 

10.44 

.08 

E. 

7 

k  Aquilae  . 

34  45-99 

.22 

•  15 

•  55 

.04 

34  45-55 

29  56.01 

10.46 

.20 

E. 

7 

y  Aquilae  . 

44  56-86 

.10 

•  56 

.04 

44  56.45 

40  6.89 

10.44 

+  .10 

E. 

7 

a  Aquilae. 

49  18.52 

.10 

•55 

•05 

49  18.09 

44  28.59 

10.50 

—  .02 

E. 

7 

P  Aquilae  . 

18  53  47.92 

.19 

0. 10 

0-55 

•05 

53  47-47 

48  57 -So 

55  10.33 

+  -17 

E. 

2 

/I  Ursae  Min.  . 

19  0  51.84 

.  IO 

3-4i 

29.05 

.06 

0  26.14 

55  6.05 

54  39-91 

.58 

E. 

7 

ft  Aquarii. 

50  30-75 

0.08 

0.56 

.08 

50  30.19 

45  40.78 

55  10.59 

•  03 

E. 

7 

v  Cygni  . 

19  57  12.74 

|  +0. 12 

+0. 16 

—  0.72 

—0.09 

57  12.09 

52  22.19 

+  55  10. 10 

+0.01 

WASHINGTON  AND  ST.  LOUIS. 


The  adopted  values  of  T0  and  0  for  each  night,  together  with  the  equations  of  con- 
ition,  normal  equations,  and  resulting  values  of  60  and  a,  are  as  follows: 


Washington,  August  5,  1870. 


Equations  of  Condition. 


T0  =  1 7’1  4™  42s 

s. 

O  rr  +  1.78  +  SO  —  5.120a 
O  rr  +  O.OI  +  SO  -(-  0.971a 
o  —  +  0.47  +  do  —  1.390  a 
o  —  -)-o.  12  +  (50 —  3.600  a 
o  =  -  0.43  +  60  +  0.923  a 
o  —  +  2.71  +  60  —  1 2.520  a 

Normal 


0  —  +  55m  1 8s. 000 

o  —  —  2.2 1  +  SO  -]-  16.860  a 
o  —  —  0.10  +  SO  -f-  0.584  a 
o  —  —  0.15  +  SO  -(-  0.724  a 
o  rr  0.00 +60  +  0.481a 
o  — —  0.09  +  SO  +  0.506  a 
o  —  —  0.09  +  50  +  0.802  a 

Equations. 


0=2+  2.02+12.00  69—  0.78  a 

o  —  —  82.06—  0.78  SO  +  485.89  a 

Hence 

111.  S. 

60  —  —  o  0.158 
a  —  +  o  0.169 
JT0  =  ES5  1 7-842  rt  os.o8o 

Washington,  August  8,  1870. 


Equations  of  Condition. 


a1  _  T  .  ui  .  .  s 

h  —  1 7  4  44 

S. 

Or:  -  O.34  +  SO  +  0.899  a 
o  rr  +  0.07  +  SO  —  0.189  a 
o  =  —  0.30  +  SO  +  0.764  a 
orr  +  o.  13  +  dO  —  0.0 1 1  a 
o  —  —  0.14  +  SO  +  0.492  a 
o  rr  +  0.14  +  60  +  0.101  a 
O  rr  +  3.29  +  SO  —  5.1  20  a 
o  rr  —  0.26  +  SO  +  0.42 1  a 
o  —  —  0.59  +  SO  +  0.971  a 
Orr—  2.41  +  SO  +  3.530  a 
O  rr  —  0.23  +  SO  +  0.448  a 


0  —  +  55“  i6s.ooo 

S. 

Orr +  O.99 +  60 —  1.390  a 

O  rr  +  0.28  +  60  —  3.600  a 
Or  —  0.56  +  60  +  0.923  a 
o  =r  +  7.96  +  60  —  1 2.520  a 
o  —  —  8.41  +  60  +  16.860  a 
Orr:  —  0.20  +  60+  0.433  a 
Orr  —  0.53  +  60+  0.894  a 
o  —  0.33  +  60  +  0.584  a 

Orr  —  0.28  +  60+  0.724  a 
o  — —  0.23  +  60+  0.481a 
Orr  — 0.33  +  60+  0.506  a 


Normal  Equations. 

Orr —  2.28  +  22.0060+  6.20  a 

o  ==  —  272.33  +  6.20  60  +  500.77  a 


SO  —  —  o  0.050 
a  —  +  o  0.543 
z/T0  rr  +  55  15.950  rb  O.071 


Hence 


DIFFERENCE  OF  LONGITUDE, 


Washington,  August  i  2,  1870. 

Equations  of  Condition. 


To  —  17"  4’"  47s 
8. 

o  —  —  0.59  +  60  +  0.676  a 
o  —  +  0.22  +  60  —  0.836  a 
o  —  —  0.68  +  69  +  0.764  a 
o  —  +  3.82  +  60 —  5.120  a 
o  —  —  0.29  -f-  60  +  0.421a 
0  =  —  0.72  +  604-  0.971  a 
03  —  0.33  +  60+  0.448  a 
o  — +  0.65  +  60 —  1.390  a 
0  =  —  0.05  +  60  —  3.600  a 
o  —  —  0.59  +  60+  0.923  a 
o  —  +  8.2 1  +60  —  1 2.520  a 


6  —  +  55m  1  38-°°o 

o  —  —  10.26  +  60  +  16.860  a 
0  =  —  7.87  +  60+16.860  a 
o  =  —  0.33  +  60  +  0.433  a 
o  —  0.42  +  60  4“  0.584  a 
o  13  —  0.51  +  60  +  0.724  ^ 
0  =  —  0.56  +  60+  0.481  a 
o  —  —  o.6o  +  60+  0.506  a 
o  3;  —  0.49  +  60+  0.540  a 
o  =  —  0.45  +  60  +  0.473  a 
o  3;  —  0.08  +  60  —  o.  1 40  a 


Normal  Equations. 

o  —  —  11.92  +  21.0060+  18.06  a 
o  3i  —  433.16  +  18.06  60  +  772.36  a 

Hence 


60  3:+  O  0.087 
«  =  +  o  0.559 
3:  +  55  13-087  db  os.  1 09 


Washington,  August  15,  1870. 

A  preliminary  reduction  of  tlie  observations  showed  that  there  was  something 
wrong  about  the  adopted  value  of  the  collimation  constant,  and  therefore  a  term  involv¬ 
ing  a  correction  to  it  has  been  introduced  in  the  equations  of  condition. 


Equations  of  Condition. 


T0=  1  yh  4U1  50s 

s. 

03: —  0.50  +  60+  1.296c —  0.0 1 1  a 
o  —  —  0.70  +  60+  1.01  6c  +  0.492  a 

o  =  +  2.33  +  60+  7.426c—  5.120  a 
03  —  0.92  +  60+  1.09  6c  +  0.971  a 

o  3=  —  0.73  +  60+  1.02  6c  +  0.448  a 

03:+  0.21+60+  2.776c —  1.390  a 
0  =  —  0.27  +  60+  1. 6 1  6c —  3.600  a 
03= —  o.8o  +  60+  1.07  6c  +  0.923  a 

03—  0.83  +  60+  1.00  6c  +  0.663  a 

03 —  8.58  +  60 — 20.72  6c  +  16.860  a 
03—  1 1.48  +  60  +  20.72  6c  +  16.860 a 


03  +  55'"  ios.ooo 

s. 

03—  0.35  +  60—  1.03  6c  + 
03 —  o.6i  +  60 —  1.06  6c  + 
03 —  0.44  +  60 —  1. 00  6c  + 
03 —  0.46  +  60 —  1.01  6c  + 
03 —  0.44  +  60 —  1.02  6c  + 
03 —  0.50  +  60 —  1.01  6c  + 
03 —  0.33  +  60 —  1. 01  6c  + 
o  3  +  30.09  +  60  —  52.89  6c  — 
03 —  0.59  +  60 —  1. 01  6c  + 
03 —  0.10+60 —  1.326c  — 


0-433  a 
0.894  a 
0.584  a 
0.724  a 
0.481  a 
0.506  a 
0.540  a 
40.680  a 
0.747  a 
0.046  a 


WASHINGTON  AND  ST.  LOUIS. 


33 


Normal  Equations. 

o  r=  +  4.oo+2i.oo(50—  44.08  dc  —  8.72  a 

or  -  1634.97  —  44.08  89  +  3738.42  8c  +  2 102.63  a 

or  —  1 578.74  —  8.72  89  +  2 102.63'  8c  +  2270.36  a 

Hence 


89  —  +  o  0.274 
8c  z r  +  o  o.  102 
a  —  +  o  0.602 
zJT0  rr  +  55  10.274  ±  Os.o85 
C  r  +  o  0.649 


Relative  Personal  Equation  of  Mr.  Frisby  and  Processor  Harhiess. — If  RT0  represents 
the  correction  to  the  Kessels  clock  at  any  given  instant,  as  determined  by  me;  and 
RT0",  the  same  correction  as  determined  by  Mr.  Frisby;  then  the  observations  of 
April  26  give, 

R  Pq  —  Rd0  +0/163 

and  those  of  August  1 2  give, 

'  RT0  =  RT0"  +  os.o8o 

The  mean  is, 

RT,-  RT0"  +  os.i2i 

which  I  adopt. 

Relative  Personal  Equation  of  Professors  Eimbeck  and  Harkness. — 111  any  case  in 
which  it  is  desired  to  determine  personal  equation,  suppose  that  a  comparison  of  the 
time-pieces  of  the  senior  and  junior  observers  shows  that  when  the  face  of  the  former 
indicates  the  time  Ts,  the  face  of  the  latter  indicates  the  time  Tq  and  let  RTS  be  the 
correction  to  the  time-piece  of  the  senior  observer,  as  determined  from  his  observa¬ 
tions;  RTj:  the  correction  to  the  time-piece  of  the  junior  observer,  as  determined  from 
his  observations;  and  m,  the  interval  by  which  the  .junior  observer  notes  the  transit  of 
an  equatorial  star  later  than  the  senior  observer.  Then,  if  RTS  and  Rl)  have  been 
determined  at  the  same  meridian, 

Ts  +  RTS  —  Tj  +  R  Tj  +  m 

and  hence 

m=Ts-Tj  +  RTs-RTj 

In  the  case  of  a  single  time-piece,  if  at  any  given  instant  its  correction  is  R T's  from 
the  observations  of  the  senior  observer,  and  RT-  from  the  observations  of  the  junior 
observer,  then 

R  Ts  —  RTj  +  m 

Considering  all  differences  of  longitude  as  essentially  positive,  if  the  senior 
observer  occupies  the 

station,  rn,  taken  with  regard  to  its  proper  sign,  must  be  j  subtracted  from  j 

the  observed  difference  of  longitude  in  order  to  free  it  from  the  effects  of  personal  equa¬ 
tion. 


(  western 
l  eastern 


5 — W  S 


34 


DIFFERENCE  OF  LONGITUDE, 


Designating  by  'J\  the  time  indicated  by  the  Kessels  clock,  and  by  1)  the  time 
indicated  by  the  chronometer  Kessels  and  Dent  No.  1287;  the  comparisons  of  time¬ 
pieces,  and  the  computation  of  m  from  the  observations  given  above  are  as  follows: 

Comparisons  of  Time-Pieces  to  determine  Personal  Equation. 


Date. 

No.  of 
Signals. 

T, 

Tj 

r,  - 

Tj 

1870. 

h. 

m.  s.  h. 

m.  s. 

m. 

t 

s. 

August 

5 

37 

21 

O 

Cl 

II 

xrs 

T 

Cl 

O 

14  11.66 

+ 

56 

0.79 

8 

37 

20 

10  11.04  =  19 

14  n.66 

55 

59-38 

12 

37 

21 

2  9.25  ==  20 

6  11.66 

55 

57-59 

15 

37 

20 

4  7-30  =  19 

S  11.66 

1  + 

55 

55-64 

Each  line  in  the  column  11  No.  of  Signals n  gives  the  number  of  signals  read  from 
the  chronograph-sheet,  the  mean  of  which  furnished  the  comparison  recorded  on  the 
same  line. 


Computation  of  the  Value  of  m. 


Date. 

A  T, 

A  Tj 

* 

AT,  - 

A  Tj 

c 
:  1 

! 

m 

1870. 

m.  s. 

m. 

s. 

m. 

s. 

m.  s. 

s. 

August  5 

-  0  43.04 

+ 

55 

17.76 

-  56 

0.80 

+  56  0.79 

- 

0.01 

8 

0  43.48 

55 

15.88 

55 

59-36 

55  59-38 

+ 

0.02 

12 

0  44.47 

55 

12.99 

55 

57-46 

55  57.59 

0.13 

15 

-  0  45.32 

+ 

55 

10.21 

-  55 

55-53 

+  55  55-64 

+ 

0.  II 

1  he  values  ot  m  apparently  divide  themselves  into  two  groups — the  results  of  the 
first  two  nights  agreeing  with  each  other,  and  the  results  of  the  last  two  nights  agree¬ 
ing  with  each  other.  However,  as  there  is  no  reason  for  supposing  that  the  observa¬ 
tions  on  one  night  are  better  than  those  on  another,  I  have  adopted  the  general  mean, 
which  is 

o 

m  —  +  os.o62  i  o8.c>2  5 

As  Professor  Eimbeck  occupied  the  western  station  during  the  exchange  of  longi¬ 
tude  signals,  this  quantity  must  be  subtracted  from  the  observed  difference  of  longitude 
in  order  to  free  it  from  personal  equation. 


VII.— EXCHANGE  OF  TIME-SIGNALS,  AND  RESULTING  DIFFERENCE 

OF  LONGITUDE. 


The  telegraph-line  between  Washington  and  St.  Louis  is  made  up  entirely  of  wire 
stretched  in  the  air,  but,  as  it  is  990  miles  long,  it  cannot  be  worked  in  a  single  circuit. 
It  was  therefore  divided  into  three  circuits,  and  the  signals  were  transmitted  from  each 
circuit  to  the  next  following  by  means  of  automatic  repeaters,  which  were  placed  at  Graf- 


WASHINGTON  AND  ST.  LOUIS. 


35 


ton  and  Cincinnati.  The  number  of  statute-miles  of  wire,  exclusive  of  that  on  the 
magnets,  and  the  amount  of  battery,  in  each  circuit,  were  as  follows: 

Washington  to  Grafton ,  335  miles:  at  Washington,  60 -modified  Grove  cells  coupled 
up  for  quantity  in  two  parallel  series  of  30  cells  each;  at  Grafton  v  50  Grove  cells. 

Grafton  to  Cincinnati ,  310  miles:  50  Grove  cells  at  Grafton;  64  Grove  cells  at 
Cincinnati. 

Cincinnati  to  St.  Louis ,  345  miles:  62  Grove  cells  at  Cincinnati;  60  Grove  cells  at 
St.  Louis. 

The  signals  employed  in  determining  the  difference  of  longitude  were  made  by 
breaking1  a  closed  galvanic  circuit;  a  method  which  seems  best  because  the  magnets 
used  in  telegraphing  are  much  more  certain  to  open  promptly  when  the  circuit  is  broken 
than  to  close  promptly  when  it  is  re-established.  This  is  true  of  a  circuit  including 
only  a  single  magnet,  but  it  applies  with  far  greater  force  when,  as  in  the  present  case, 
the  signals  are  transmitted  through  several  circuits  by  means  of  repeaters. 

As  the  observer  at  St.  Louis  had  neither  a  clock,  a  break  circuit  chronometer,  nor 
a  chronograph,  it  was  necessary  to  employ  other  means  in  making  the  telegraphic  com¬ 
parisons  of  time-pieces  there.  The  plan  adopted  is  fully  explained  in  the 


PROGRAMME  FOlt  THE  EXCHANGE  OF  LONGITUDE-SIGNALS. 


1.  Local  sidereal  time  will  be  determined  at  each  station  by  observing-  transits  of  stars  in  the 
usual  manner. 

As  the  telegraph-wires  do  not  extend  to  the  observing-station  at  St.  Louis,  whenever  signals 
are  to  be  exchanged  it  will  be  necessary  for  the  observer  there  to  go  to  the  telegraph-office  in  the 
Merchant’s  Exchange,  carrying  with  him  a  mean  time  box-chronometer  beating  half-seconds.  The 
distance  between  the  observing-station  and  the  telegraph-office  is  about  one  and  a  half  miles, 
and  to  avoid  the  chance  of  undetected  tripping  of  the  chronometer  while  being  carried,  it  must 
be  compared  with  the  standard  sidereal  chronometer  each  evening  immediately  before  starting  from, 
and  immediately  after  returning  to,  the  observing-station. 

2.  Every  afternoon  the  observer  at  St.  Louis  will  notify  the  observer  at  Washington  as  to  the 
state  of  the  weather,  and  if  it  is  clear  at  both  places  arrangements  will  be  made  to  exchange  signals 
in  the  evening.  The  hour  of  making  the  exchange  will  necessarily  depend  very  much  upon  the 
convenience  of  the  telegraph  company,  but  it  will  usually  be  practicable  to  obtain  the  use  of  the 
wires  some  time  between  10  p.  m.  and  midnight. 

3.  The  telegraph-office  in  the  Merchant’s  Exchange  at  St.  Louis,  and  the  United  States  Naval 
Observatory  at  Washington,  having  been  put  in  communication,  the  observer  at  the  former  will 
ask  the  observer  at  the  latter  if  he  is  ready  to  receive  signals,  and,  upon  getting  an  affirmative 
reply,  the  St.  Louis  observer  will  wait  until  his  mean-time  chronometer  indicates  50  seconds,  and 
then  he  will  send  a  rattle  by  means  of  his  break-circuit  key.  This  rattle  will  consist  of  ten  or  fifteen 
dots  made  at  the  rate  of  about  five  per  second.  At  the  beginning  of  the  next  minute  he  will  com¬ 
mence  sending  his  first  series  of  signals.  This  will  consist  of  thirteen  taps  on  his  key,  made  in  exact 
coincidence  with  the  beats  of  his  chronometer  at  o,  5,  10,  15,  20,  25,  30,  35,  40,  45,  50,  55,  and  o 
seconds;  a  pause  of  five  seconds,  and  a  rattle.  At  the  beginning  of  the  next  minute  he  will  com¬ 
mence  sending  his  second  series  of  signals.  This  will  consist  of  eleven  taps  on  his  key,  made  in 
coincidence  with  the  beats  of  his  chronometer  at  o,  1,  2,  3,  4,  5,  6,  7,  8,  9,  and  10  seconds;  a  pause 
of  five  seconds,  and  a  rattle.  At  the  beginning  of  the  next  minute  he  will  commence  sending  his 
third  series  of  signals.  This  will  consist  of  thirteen  taps  on  his  key,  made  in  coincidence  with  the 
beats  of  his  chronometer  at  o,  10,  20,  30,  40,  50,  o,  10,  20,  30,  40,  50,  and  o  seconds;  a  pause  of  five 
seconds,  and  a  rattle.  The  three  series  of  signals,  from  the  beginning  of  the  first  rattle  to  the  end 
of  the  last  rattle,  will  occupy  about  four  minutes  and  twenty  seconds;  and  immediately  upon  their 


36 


DIFFERENCE  OF  LONGITUDE, 


completion  the  observer  at  Washington  will  notify  the  observer  at  St.  Louis  whether  or  not  they 
have  been  properly  received.  If  they  have  not  been,  they  will  be  repeated  ;  if  they  have  been,  the 
observer  at  St.  Louis  will  telegraph  to  the  observer  at  Washington  the  hour  and  minute  indicated 
by  the  chronometer  at  the  beginning  of  the  first  series.  The  observer  at  St.  Louis  will  of  course 
preserve  a  record  of  the  hour  and  minute  indicated  by  the  chronometer  at  the  commencement  of 
each  of  the  series  of  signals. 

These  signals  will  all  be  transmitted  to  Washington,  where  they  will  record  themselves  upon 
the  chronograph  sheet  along  with  the  beats  of  the  Washington  clock,  and,  as  the  probable  error  of 
a  single  signal  is  only  about  T  os.o34,  they  will  furnish  a  very  accurate  comparison  of  time-pieces. 

4.  As  soon  as  the  observer  at  Washington  has  been  notified  of  the  hour  and  minute  corre¬ 
sponding  to  the  beginning  of  the  first  series  of  signals  from  St.  Louis,  he  will  ask  the  observer 
there  if  he  is  ready  to  receive  signals  from  Washington,  and  upon  receiving  an  affirmative  reply  he 
will  connect  the  Washington  sidereal  clock  with  the  telegraph-line  in  such  a  manner  that  its  pendu¬ 
lum  will  break  the  circuit  for  somewhat  less  than  one-tenth  of  a  second  every  time  it  passes  the 
central  point  of  its  arc,  thus  making  a  break  once  every  second.  In  addition,  the  beginning  of  each 
miuute  will  be  marked  by  a  double  break — that  is,  by  a  break  interpolated  midway  between  the 
break  corresponding  to  o  seconds  and  that  corresponding  to  1  second. 

These  signals  will  be  transmitted  to  St.  Louis  and  there  rendered  audible  bj-  means  of  a 
sounder  so  adjusted  that  its  back  stroke  is  much  louder  than  its  forward  one.  Sitting  beside  this 
sounder,  and  keeping  his  eye  upon  his  mean  time  chronometer,  the  observer  at  St.  Louis  will  wait 
until  the  back  stroke1  of  the  sounder  coincides  with  the  beat  of  the  chronometer;  and  when  this 
occurs  he  will  note  the  time  indicated  by  the  latter,  and  also  the  time  of  arrival  of  the  next  follow¬ 
ing  double  break.  Three  such  coincidences  will  be  recorded,  and,  as  they  occur  at  intervals  of  about 
three  minutes,  the  time  required  for  so  doing  will  not  generally  exceed  twelve  minutes.  As  soon 
as  the  double  break  following  the  third  coincidence  has  been  received,  the  observer  at  St.  Louis  will 
open  the  circuit  and  ask  the  observer  at  Washington  what  hour  and  minute  of  his  clock  corresponded 
to  the  break  in  question.  The  observer  at  Washington  having  furnished  the  desired  information, 
the  two  stations  will  bid  each  other  “good  night,”  and  this  will  close  the  exchanges  for  the  evening. 

N.  B. — Although  there  will  generally  be  an  uncertainty  of  three  or  four  seconds  as  to  the 
exact  instant  when  the  beat  of  the  sounder  coincides  with  that  of  the  chronometer,  still  special 
care  must  always  be  taken  to  note  whether  the  coincidence  occurs  at  a  whole  or  at  a  half-second 
beat  of  the  chronometer.  "  , 

The  record  of  signals  received  at  St.  Louis,  from  Washington,  on  the  evening 
of  April  12,  together  with  their  reduction,  is  appended  in  order  to  show  how  the  com¬ 
parison  of  time-pieces  is  deduced  from  the  coincidences  of  beats  observed  in  the  manner 
just  described. 

Coincidence  of  breaks  with  beats  of  chronometer.  Next  follow  ing  double  break. 


h.  tn. 

s. 

s. 

to 

45-0 

32.0 

20 

44-5 

31-5 

23 

40.0 

3 1.0  —  14’1  42™  os.o  Wash.  Clock. 

As  the  double  break  corresponds  to  o  seconds  of  the  Washington  clock,  if  from 
the  seconds  of  the  time  of  coincidence  of  beats,  (increased  by  60  when  necessary,)  the 
seconds  of  the  time  of  the  next  following  double  break  are  subtracted,  the  remainder 
will  be  the  seconds  indicated  by  the  face  of  the  Washington  clock  at  the  time  of  the 
coincidence  of  beats.  Thus,  for  the  first  coincidence  recorded  aboye, 

45s-0  —  32S-Q  =  i3s-o 

1  The  back  stroke  is  used  because  it  corresponds  to  the  break.  The  forward  stroke  corresponds  to  the  subsequent 

closing  of  the  circuit. 


WASHINGTON  AND  ST.  LOUIS. 


37 


The  last  recorded  coincidence  and  doable  break  give,  not  only  the  seconds  of  the 
Washington  clock,  but  the  hour  and  minute  also  ;  thus  furnishing  the  means  of  sup¬ 
plying  the  hour  and  minute  to  each  of  the  other  coincidences.  Applying  this  pro¬ 
cess  to  the  record  given  above,  we  obtain : 

Kessels  Clock.  Chronometer  Dent  No.  2748. 


h.  m. 

S. 

ll.  111. 

s. 

H  35 

13.0  z= 

12  17 

45-o 

38 

13.O  = 

20 

44-5 

41 

9.0  =z 

23 

40.0 

If  we  let 

AX  —  difference  of  longitude  between  two  stations;  west  longitudes  being  taken 
as  positive; 

Te  —  time  by  face  of  eastern  clock  when  it  sends  a  signal,  and 

Tw  —  time  by  face  of  western  clock  when  that  signal  is  received  at  the  western 

station ; 

T'w  —  time  by  face  of  western  clock  when  it  sends  a  signal,  and 

T'e  =  time  by  face  of  eastern  clock  when  that  signal  is  received  at  the  eastern 
station ; 

t.—  time  occupied  in  the  passage  of  a  signal  from  one  station  to  the  other; 

ATe,  z 1TW ,  AT'e,  A T'w  —  respectively,  the  corrections  necessary  to  reduce  the 
times  indicated  by  the  faces  of  the  eastern  and  western  clocks  to  true  local  time  at 

the  instants  Te,  Tw ,  T'e,  T'w,  then,  neglecting  personal  equation,  when  the  eastern 

clock  sends  and  the  signals  are  received  at  the  western  station,  we  have 

AX  -  t  =  (T-Tw)  +  (AT-ATW) 

and  when  the  western  clock  sends,  and  the  signals  are  received  at  the  eastern  station, 
we  have 

zbl  +  t  =  ( T'e-T'w )  +  (. AT'-AT'W ) 

Hence 

+  (^Te-ATW)  +  (  AT'e  —  A T'w) 

2  '  2 

-  (Te—  Tl0)  (AT'e-AT'w)-(ATe-ATw) 

2  2 

If  the  rates  of  the  clocks  are  small,  the  second  term  in  the  expression  for  the  value 
of  t  may  usually  be  neglected. 

The  following  are  the  results  of  the  telegraphic  comparisons  of  time-pieced,  both 
at  Washington  and  St.  Louis,  together  with  their  reduction  by  means  of  the  formulae 
just  given,  used  in  connection  with  the  data  contained  in  the  preceding  pages.  By 
way  of  explanation  it  is  only  necessary  to  remark  that  each  line  in  the  column  headed 
11  No.  of  Signals ”  gives  the  number  of  signals  read  off  from  the  chronograph-sheet,  the 
mean  of  which  furnished  the  comparison  recorded  on  the  same  line. 


38 


DIFFERENCE  OF  LONGITUDE, 


Comparisons  of  Time- Pieces  obtained  bg  reading  off  the  Washington  Chronograph-Sheets. 


Date. 

No.  of 
Signals. 

j  Kessels  Clock 
at  Washington. 

Dent  2748 
at  St.  Louis. 

Means. 

T' 

,  - 

T'u 

1870. 

h. 

m. 

s. 

h.  m. 

s.  h. 

m. 

s. 

h. 

m. 

s. 

h. 

m. 

- ! 

s.  j 

April  12 

13 

14 

3 

53.22  == 

11  46 

30.  <Jo 

. 

I  I 

5 

27.94  = 

48 

4-50  14 

5 

35.00  = 

I  I 

48 

n.50 

!  + 

2 

17 

23.50 

13 

7 

23.83  = 

50 

0.00 

April  23 

13 

14 

36 

52.50  = 

11  36 

30.06 

II 

38 

27.79  = 

38 

5-oo  ,  14 

38 

34-45  = 

I  I 

38 

n.67 

+ 

3 

0 

22.78 

13 

40 

23.06  = 

40 

0.00  1 

April  26 

13 

14 

37 

34-2S  - 

11  25 

30.00 

I  I 

39 

9.62  == 

27 

5.00  ,  14 

39 

16.26  = 

II 

27 

n.67 

+ 

3 

12 

4-59 

13 

41 

4.88  = 

29 

0.00 

April  30 

13 

14 

59 

13-83.= 

11  31 

30.00 

II 

15 

0 

49.12  = 

33 

5-oo  ;  15 

0 

55-78  = 

I  I 

33 

n.67 

+ 

3 

27 

44.11 

_ _ _ 

13 

2 

44-39  = 

35 

0.00 

Comparisons  oj  Time- Pieces  obtained  bg  observing  Coincidences  of  Peats  at  St.  Loam. 


Date. 

No.  of 
Coinci¬ 
dences. 

Kessels  Clock 
at  Washington. 

Dent  2748 
at  St.  Louis. 

Means. 

Tt  - 

T,r 

1870. 

h. 

m. 

s. 

h.  m. 

S. 

h. 

m. 

s. 

h. 

m. 

s. 

h.  m. 

s. 

April  12 

1 

14 

35 

13.00  - 

12  17 

45.00 

I 

38 

13.00  = 

20 

44-50 

14 

38 

n.67  = 

12 

20 

43-17 

+ 

2  17 

28.50 

I 

41 

9.00  = 

23 

40.00 

April  23 

I 

14 

47 

39.00  = 

n  47 

15.00 

I 

50 

45.00  = 

50 

20.50 

14 

50 

44.67  - 

II 

5<1 

20.17 

4- 

3  0 

24-50 

I 

53 

50.00  = 

53 

25.00 

April  26 

I 

14 

22 

22.00  = 

II  10 

20.50 

I 

25 

27.00  = 

13 

25.00 

14 

25 

27-33  = 

I  l 

13 

25-33 

+ 

3  12 

2.00 

I 

28 

33.00  = 

l6 

30.50 

April  30 

I 

14 

44 

1 1. 00  == 

1 1  16 

30.00 

I 

47 

17.00  == 

19 

35-50 

14 

47 

15.00  = 

I  I 

!9 

33-50 

+ 

3  27 

41.50 

I 

50 

17.00  = 

22 

35-00 

WASHINGTON  AND  ST.  LOUIS. 


39 


Clock  and  Chronometer  Corrections  at  the  Times  of  the  Exchange  of  Signals,  computed  by 
means  of  the  Formnlce  contained  in  Tables  III  and  V. 


Date. 

Kessels  Clock 
at  Washington. 

Dent  2748 
at  St.  Louis. 

h  T'e  •—  A  T'„, 

j 

at;  -  a rw 

1870. 

h.  m.  s. 

h.  m.  s. 

h.  m.  s. 

h.  m.  s. 

April  12 

—  0  0  1.995 

+  1  24  44.431 

—  1  24  46.426 

2.002 

49-735 

-  1  24  51-737 

April  23 

—  0  0  5.616 

+2  7  40.133 

-  2  7  45-754 

5.623 

42.114 

-  2  7  47-737 

April  26 

—  0  0  7.188 

+  2  19  20.338 

—  2  19  27.526 

7-179 

18.075 

—  2  19  25.254 

April  30 

—  0  0  8.929 

4  2  34  58.122 

-  2  35  7.051 

. 

' 

8.926 

55.896 

—  2  35  4.822 

Observed  Values  of  the  Difference  of  Longitude  between  Washington  and  St.  Louis,  and  of 
the  Time  occupied  in  the  passage  of  a  Galvan  ic  Signal  between  those  Cities. 


Date. 

i(T'e  - 

T'O 

wo  - 

7V)  T\  — 

A  T'v) 

WO- 

A  TV) 

A  T 

t 

1870. 

h.  m. 

s. 

h. 

m. 

s.  h.  IT). 

s. 

h. 

m. 

s. 

h.  m.  s. 

s. 

April  12 

+  x  8 

41.750 

4-  I 

8 

44.250  —  0  42 

23.213 

—  0 

42 

25.868  + 

0  52  36.919 

+  0.155 

23 

1  30 

11.390 

I 

30 

12.250  1  3 

52-877 

I 

3 

53-868 

36.895 

.131 

26 

1  36 

2.295 

I 

36 

I. 000  !  I  9 

43-763 

I 

9 

42.627 

36.905 

•  159 

30 

+  1  43 

52.055 

+  I 

43 

50.750  -  I  17 

1 

33-526 

—  I 

17 

32.411  i  + 

0  52  36.868 

+  o.igo 

The  time  occupied  in  the  passage  of  a  signal  between  the  two  cities  seems  to  have 
varied  considerably  on  different  nights;  probably  owing  to  slight  changes  in  the  adjust¬ 
ments  of  the  repeaters  connecting  the  several  circuits.  Of  course  these  observations 
give  no  clew  to  the  speed  of  a  galvanic  wave  propagated  in  a  continuous  conductor. 

Taking  the  mean  of  the  values  of  A,  we  find  that  the  observing-station  at  St. 
Louis  is  oh  52™  36s.897  M  os.oo7 

west  of  the  transit  circle  at  Washington.  This  result  requires  two  small  corrections: 
1  st,  for  personal  equation,  Professor  Eimbeck  observing  the  transit  of  an  equatorial  star 
os.o62  ±01025  later  than  myself;  and,  2d,  to  refer  the  difference  of  longitude  to  the 
center  of  the  dome  of  this  Observatory,  that  point  being  77.8  feet  —  os.o66  east  of  the 
transit  circle.  Making  these  corrections,  and  having  regard  to  the  probable  error  of 
the  personal  equation,  our  final  result  is  that 

The  Observing-  Station  at  St.  Louis,  in  the  Washington  University 
grounds,  on  St.  Charles  street,  between  Seventeenth  and  Eighteenth  streets, 
is  west  of  the  center  of  the  Dome  of  the  United  States  Naval  Observatory 
at  Washington 

0b  ^ 2111  36s, 90  ±  0s, 026 

Very  respectfully,  WM.  HARKNESS, 

Professor  of  Mathematics,  U.  S.  Navy. 

Rear-Admiral  B.  F.  Sands,  U.  S.  N., 

Superintendent  U.  S.  Naval  Observatory,  Washington,  D.  C. 


HIMHiHI 


